You don’t mention a scale, but I can answer for N scale.
Alright, shoot!
A #5 has a diverging route that is sharper then a #7. The curved track moves away from the straight track at a sharper angle.
Larger turnouts (number wise) always look better and are easier on the rolling stock. Smaller numbered turnouts are used where space is a premium. Most rolling stock will make it through a #5, but some won’t do it at speed. You might use #5’s in the yard and on industrial sidings, and #7’s for passing sidings, branchline entrances, and other such routes that see a lot of traffic or higher speed traffic.
For the N scale code 55 track a 30"r curve will bring a #5 parallel and a 72" curve will do the same for a #7.
Most N scalers go with a track centerline to track centerline distance of 1 1/4" to 1 1/2".
You know how a knight in chess moves two down and one over. Think of the turnouts that way. The diverging track on a #5 turnout would be 5 down and one over from the straight track. A #7 would be 7 down and one over. The bigger the number, the more gentle the divergence. Faster moving trains and larger trains do better with higher numbered turnouts.
I should mention that although the #5 turnouts are semi-common, the most commonly manufactured by model companies are the #4, #6, & #8.
Maybe there is a set piece, but I just use flex track. It really depends on the manufacturer of the track.
You want to get your fingers in. This will be debated. It also matters which scale you are modeling. For HO I like 2".
Thanks guys! Yeah I am playing with N…Sorry about not mentioning that! I’m planning a switch to N from HO here in the near future, and I’m just playing around with what I can fit into a small space. I’ve almost got something going here so I’ll try to post a picture of it sometime tomorrow for a critique.