Which prayers are to be recited aloud and which silently, and what is the wisdom behind silent prayer?

The loud prayers are Maghrib, 'Isha, and Fajr, and the silent ones are Dhuhr and 'Asr. We pray them silently because the Prophet, peace and blessings be upon him, prayed them silently, and we must emulate him, as Allah Almighty says: (There has certainly been for you in the Messenger of Allah an excellent pattern) and the Prophet, peace and blessings be upon him, said: (Pray as you have seen me pray).