Hmmmm, bike fit depends on a lot of factors besides just seat tube length, which is what the "size" of a bike is generally based on. You really need to look over the total geometry of the bicycle, including stand over and top tube length especially to see what size of bicycle will fit you.
I would suspect at 5'1" a 50 would pretty much always be too large for you. I am 5'0 and my bikes are a 44cm with 700c wheels, and a 47cm with 650c wheels. I am short torso'd and armed so I need a smaller size frame than all people of my size, but a 50cm would be seriously large. I'm not ever sure I could stand over a 50 and I have around a 29" inseam - which is pretty long for a shorty like myself.
Don't go with this bike just because it is cheap - if you buy a bike that is too large for yourself you will be uncomfortable, slow, have trouble climbing hills and you'll end up not liking the sport. I would encourage you to go to a local bike shop, get fit and work with them to find a bike that is in your budget.