You really need to know the exact year and model of the bike. Then you can look at the sizing recommended by the manufacturer for that model. A size bike that fits you in one model of bike might not be the size you need for another model of bike. But trying out the bike in person is a good way to tell. But if you are inexperienced, then you probably should have someone that knows with you.

At 5'-10" you'll be safe with a M size or 54 - 56 cm, but again, depending on the model you might be okay with larger or even smaller size. Some people can ride different size bikes a few sizes from what's considered ideal for them with no fit issues. Some people have fit problems with any size bike.

Tire size, which it seems like you are going by plays only a small part in the big scheme of fitting you to the bike. It'll alter how you perceive the handling of the bike, but not whether it fits you.

Welcome to BF.