What is the ruling on someone who abstained from prayer for five days due to janabah and the inability to perform ghusl in the hospital, and what must he do?

Prayer is never forsaken. What was obligatory upon you was to perform ghusl and pray on time. If you were unable to perform ghusl due to a legitimate Shar’i excuse (such as illness), then it was obligatory upon you to perform tayammum and pray. As for embarrassment and shyness, they are not excuses. Now, you must offer sincere repentance and make up all the missed prayers.