Be sure you have your measurements correct. A guy who is 5'10 normally has a total leg length of about 34 inches from the floor to the public bone. To measure your leg length, find a book that is about 12 inches tall and four inches wide. Pull it up against your crotch until it is uncomfortable. Then pull the book up another inch, until it is REALLY uncomfortable. Have a friend measure the distance from the top of the book to the floor. Do this eight or ten times. You will get a variety of results. The highest measurement is your total leg length.
If your total leg length is 34 inches, you would start by looking a bikes with about a 32 inch "standover". Measure the bikes "standover" about one inch behind the stem, measuring from the top of the top tube to the ground. If a bike has a 32 inch standover and you have a 34 inch leg, the top tube will lightly brush your jeans when you stand flat footed with your belt buckle an inch behind the stem.
When bikes use "traditional" sizing (which few do these days) the "average" 5'10" guy got a good fit on bikes in the 56 to 60 range (56 for short rides and racing...60 for touring and commuting ).
The key to bike fit is to buy from a good bike shop. The techs at a good shop have experience in fitting people both for their size and their riding style. Any good bike shop can special order a "track bike" or single speed bike that is of higher quality than those sold on the internet for "99% off factory list price".