What is the ruling on saying "Sami'a Allahu liman hamidah" (Allah hears those who praise Him) after rising from prostration instead of bowing, and what are the implications of this, such as adding an extra rak'ah (unit of prayer), and what is required of someone who has done this multiple times in the past?

The saying "Samia Allahu liman hamidah" (Allah hears the one who praises Him) after rising from prostration is a prescribed remembrance, but it is not in its proper place [at that point in the prayer]. However, it does not invalidate the prayer or the rak'ah. The fifth rak'ah added out of ignorance does not invalidate the prayer. Therefore, your previous prayers are valid, and you do not need to repeat them. It is incumbent upon a Muslim to learn the obligatory acts of purification, prayer, and similar matters.