The timings for prayer are clearly explained in the Islamic texts, and they are based on things that are visible, and can be understood by any one with a little sense.
The time for Fajr begins with the breaking of the true dawn, in which the light spreads horizontally along the horizon, to the right and left.
The time for Zuhr begins when the sun moves from the middle of the sky.
The time for ‘Asr begins when the shadow of an object is equal in length to the object itself plus its shadow at the time when the sun is at its zenith.
The time for Maghrib begins when the disk of the sun disappears completely beneath the horizon.
Al-Nawawi said: What matters is when its disk disappears completely, and after it has disappeared completely the rays that remain do not matter; rather the time for the prayer begins even though those rays are still present. End quote. Al-Majmoo’, 4/169
Ibn Taymiyah said: At that time, the fasting person may break his fast and the time when prayer is disallowed ends, and what is left of red light on the horizon does not affect any ruling.
The time for ‘Isha’ begins when the red glow disappears from the horizon.
For more information on the timings of prayer, please see the answer to question number 9940.
You have to try hard to recognise the signs and act in accordance with them. If that is too difficult for you, then there is nothing wrong with following one of the mosques, if you trust the religious commitment and sincerity of the people in charge.
And Allah knows best.