I am the exact same hirght and weight as you and I ride a 5'8 most of the time but i am now going more for my 5'10. It also depends on how wide and thick your board is, my 5'10 is a squash tail and 18.5 x 2 1/8 and floats me well.
I was at 135 about 3 years ago and i still rode a longer board. imho surfing is not about learning to ride one type of board, but rather being able to ride any board... so if the waves are smaller, i am going to take out my fish or my longboard. balance and variety
im 5'9, ive been surfing for many many years, but in my quiver i have a 9'0 eaton longboard, a 6'2 CB shortboard, a 5'5 natural art shortboard, 6'3 Rainbow retro fish, and a 9'2 dewey webber longboard from the 60's. I can ride all of them, so if i can ride a 5'5 and im 5'9 i think youll be able to ride your board, but if your learning its probably going to be tough.