Is it permissible for me not to perform the five daily prayers and the Friday prayer because I am compelled not to leave the institute due to classes extending throughout the day?

Abandoning the Friday prayer without a valid excuse is considered a major sin. The Prophet, peace and blessings be upon him, said: "Indeed, some people will cease neglecting the Friday prayers, or Allah will seal their hearts, and then they will be among the heedless," and "Whoever neglects three Friday prayers out of complacency, Allah will seal his heart." The excuses that permit absence from Friday prayer and congregational prayer include: severe mud and rain, illness, nursing a relative, fear for one's wealth or self, nakedness, and consuming something that harms worshippers.

Furthermore, delaying prayer beyond its prescribed time is forbidden, as Allah Almighty says: "Then, there succeeded them a generation who neglected prayers and pursued desires; so they are going to meet Ghayyā" and "So woe unto those performers of Salāt (prayers) Those who delay their Salāt (from their stated fixed times)." If delaying prayer is not permissible during war, then it is even more impermissible during peace.

Based on this, studying at an institute that prevents Friday prayer or delays prayer beyond its prescribed time is not permissible, and one must leave it and repent to Allah.