I am wondering if Frigidaire FAX054P7A 5000 BTU Window Air Conditioner will be sufficient for my 15 Ft by 10 Ft (total bedroom area 150 square feet) bedroom as far as adequate cooling is concerned?

The Frigidaire FAX054P7A is designed to cool a room up to 150 square feet, so your bedroom size is just at the limit of it's capacity. Assuming you aren't someone who gets exceptionally hot, this unit should work fine.