Does delaying a prayer until hearing the adhan for the next prayer render it outside its prescribed time, and is the reward of one who prays immediately upon hearing the adhan equal to that of one who prays a short while before the entry of the next prayer's time?

For prayers, there are optional and necessary times. It is desirable to perform them at the beginning of their time, due to the promptness in obedience that it entails, and this is better than performing them at the end of it. One who prays immediately after the adhan does not have the same reward as one who prays before the time of the next prayer enters. The latter may be sinful, or at the very least, may have missed the virtue of the early time. It is obligatory for a man to perform prayer in congregation in the mosque, while for a woman, it is better for her to pray in her home.