Okay, I haven't been there for a while, but I have been there. Now, my 5% body fat was not like that of the professional bodybuilders -- I did not have the extra muscle to go with it -- and mine resulted from a lot of serious sports training including endurance running. Unfortunately, this amount of aerobic and anaerobic training also burns some muscle. It's easy to appreciate how difficult it is to bulk up substantially and get this low in body fat. It takes a lot of work and I now settle for a more body fat and more muscle.
Naturally, if you're a bodybuilder or fitness weight trainer, you can aim for low body fat to expose your ab muscles and to help define those other muscles you've built. Men can get down to around 5% and women to about 12% body fat. Below those numbers you really have to be careful that some basic physiological and hormone systems aren't disrupted to the extent that you get ill. The immune system can suffer, and in women, periods can go missing and bone health can be affected adversely.
As to what it feels like, well . . . it's a little difficult to explain, but you feel "light and powerful," that was my experience -- as if there's nothing in the way of your muscle contractions. It's a positive feeling as long as you stay healthy. My total cholesterol was around 150 mg/dl (3.9 mmol/L) with relatively high HDL and very low triglycerides. Attaining very low body fat levels with exercise can drop total cholesterol, improve good/bad cholesterol ratios and lower triglycerides in the blood -- all good numbers for a healthy heart. But you still need to have a doctor assess your cholesterol risk. Not everyone responds in the same way.
If you want to know how to measure body fat, here's an article on just how to do it. All About Body Fat Measurement.