I'm a fit 24 year old and have been 5'6 160lbs since I was 16. Is this too much weight for my height? I've been +/- 5 pounds since then.

A bit over. At 5'6" and 160 lbs your bmi is 25.8, which is a bit over the recommended 24.9 or lower. Your recommended weight range is 115-154 lbs. So by losing 6 lbs you can get down to a bmi of 24.9. It's not necessary to get down to 115. As long as you're eating healthy and exercising, being within the range is good.
66 inches and 160lbs. You do not have a big problem, your bmi is 25.8.You are slightly over weight and losing 5 lbs will bring you in the healthy range.So good luck and do it.