Although all Islamic laws are a result of the benefits or disadvantages and harms that back them, and they all have a particular reason behind each and every one of them, discovering the exact reason in detail for every one of them and knowing that this is all there is to it, is extremely difficult. The most we can do is give some general guidelines regarding these laws, and what we mean here by ‘general’ isn't that there aren't any exceptions either. In addition to these general points, certain reasons for praying in specific times have been pointed to, such as the saying that goes: Allah wants His remembrance and worship to take place before anything else, and for prayer to be with what we start the important tasks of our life, which begin at these same five times. Also, it is said that Allah (swt) wants to show the Muslims the importance and value of paying attention to time through such.
To get your answer, several points need to be considered:
1- Based on the true theory that Shia scholars and ulema believe in, the laws Allah (swt) legislates are all based on the benefits they entail or the harms and disadvantages they prevent, in other words, if something is made wajib, it is because of the one or many important or crucial benefits it entails, and if something is made mustahabb, it is because it entails non-crucial benefits. The same goes for haram and makruh acts; if something is haram, it means that it has one or several extremely bad and harmful outcomes, and if something is makruh, it shows that the bad things it entails aren't very severe or harmful. As for acts that neither have a dominating benefit nor a dominating harm are mubah (which means permissible). One thing that must be noted is that when we say benefit or harm, it has a vast meaning that covers more than just worldly ones; it has to do with all perspectives and existential dimensions of man.
2- Although the abovementioned principle that says Islamic laws follow the real benefits and harms certain actions entail is one accepted by all and is for sure, nevertheless, discovering exactly why and what reasons cause a ruling is extremely hard and challenging because:
Firstly: Such a task calls for a great deal of knowledge in many many different fields.
And Secondly: No matter how much man's knowledge develops, what he knows will be a drop in comparison to what remains unknown to him and he hasn’t discovered yet “…and you have not been given of knowledge except a little”.
Maybe the reason why our imams didn’t explain the reasons for these laws was because the scientific and scholarly status of the world back then totally differed from now and the people then wouldn’t understand anything that was being said to them, and this might have even led to a backfire, resulting in their dislike of the religion. Imam Ali (as) says: “People are the enemy of what they do not know.” This led to the imams not engaging in such matters.
Add to that the fact that religion and its laws pursue the goal of us becoming good people and building ourselves both in spiritual matters and in knowledge, and to be free of bad knowledge and actions, and this goal is reachable through acting upon religion, even if we don’t know why religion has asked us to do certain things, the same way we listen to the doctor even though we might not know exactly why he has prescribed a certain drug and know that we will get better. The believers know that religious commands and laws come from individuals who are infallible and whose knowledge comes from above, making it flawless, therefore they are sure the goal of their creation is obtainable through acting upon these orders.
3- Although finding the exact reasons for Islamic laws is very difficult and taxing, it is possible to present some general guidelines regarding them. Of course generality in law-related matters differs from generality in philosophy; in philosophy if something is general it means that there are no exceptions, and that is not the case in law. What is meant by general guidelines here, is that they usually apply, but there also might be exceptions sometimes.
In addition to these general points, particular reasons have also been pointed to in traditions regarding praying in these specific times:
a) Regarding the reasoning behind the times of prayer, Imam Ridha (as) says: “Allah chose these times, since they were recognized by the people, and because the time for Asr prayer wasn’t recognized, it was set for after the Dhuhr prayer.”
b) Allah (swt) willed that His worship take place before anything we do, and that is why He set these times for prayer. The morning prayer was set before the day and our work in it begins, Dhuhr was set before our rest from a day’s work, Asr was set before the second round of work after resting, Maghrib was set for after returning home and putting down worldly adornments, and Isha prayer was the beginning of the end of daily chores and the onset of nightly rest and sleep. This makes prayer the beginning of each important stage of one’s life, and it has been set for keeping the remembrance of Allah and His worship alive.
c) A hadith by the noble prophet (pbuh) regarding the necessity of upholding the prayers in their respective five times reads: “When the sun reaches the zawal point [the point in which the sun reaches its highest point in the sky and begins its way downwards] there is a ring in which it enters which is the zawal time. At this time, everything under the ʻArsh praises my Lord. It is a time in which my Lord sends his blessings unto me. The exalted Lord has made prayer mandatory on me and my nation saying: “Maintain the prayer from the sun's decline till the darkness of the night”. On the Day of Judgment, when they bring the Fire, there won't be a believer who was given the tawfiq [success] to be prostrating or bowing down in this time whose body will not be made forbidden onto the Hellfire by Allah. The time of Asr prayer is the time in which Adam ate from the tree and was excused from the garden and [Allah] ordered his progeny to pray this prayer till the Day of Judgment and [also] chose it for my nation; it is the most beloved prayer in His eyes and He advised me to particularly observe it among all prayers. The Maghrib prayer is in a time when Allah accepted Adam’s repentance…Adam offered three rak’ats of prayer; one rak’at for his own sin, one for Hawwa’s and one for his repentance, Allah made these three rak’ats wajib on my nation. This is the time in which supplications are answered, my Lord has promised me that he will answer the supplications of anyone who calls Him in that time, this is one those prayers that my Lord has ordered me and has said: “Immaculate is the Lord, when you enter the morning and at the end of the day, the Isha prayer is because the grave is dark and there is darkness on the Day of Judgment; my Lord has obliged this prayer so their graves are illuminated and they are granted light on the Sirat [the bridge that crosses over Hell on the Day of Judgment that everyone must cross]; for every step they take for the Isha prayer Allah forbids their body to the Fire. This is a prayer made obligatory on all prophets before me. The Fajr prayer is because the sun rises on the two horns of Shaytan (which apparently is metaphorical of the fact that with the rise of the sun, which is when the people wake up, Shaytan’s activity begins) and Allah ordered me to pray before the sun rises and for my nation to prostrate for Allah before the disbelievers prostrate to the sun. Rushing for it is more beloved in the eyes of Allah; it is a prayer that the angels are a witness of day and night.
In addition, upholding prayer, especially in the beginning of its time, and the repetitive obligation of it throughout the day and night, aside from it making the individual thankful, brings about high personal and social order, and also unity and uniformity and glory to the Islamic society and is a means of preserving divine sacraments from being forgotten and altered.
 “و ما اوتیتم من العلم الا قلیلاٌ” Isra:85.
 “الناس اعداء ما جهلوا” Gozideye Mizanul-Hikmah, vol. 1, pg. 214.
 With help from Question 1967 (website: 2070).
 Wasa’il al-Shia, vol. 4, pp. 15 and 161, the chapter of prayer, the book of the number of obligations, the book of the obligation of prayer, hadiths 7 and 8.
 Wasa’il al-Shia, book number 10 of the number of obligations, hadiths 1-5 and 7-9.
 Ibid, book number 6 of the number of obligations, hadiths 3-8, Ibid, book number 10 of the book of times of prayer, hadith 11.
 Amali, Sheikh Saduq (Farsi translation by Kamare’i), pg. 190, text.
 Related index: The meaning and effects of prayer, Question 2997 (website: 3242).