Almost forgot to mention, you might want to look into the Pentium G4560. It offer's ~90% of the performance of the i3 7100 for less than 60% of the cost. Intel i3's are kinda poor value right now, for the most part you're better off either getting a Pentium for a lot less money, or saving up and getting an i5.
The G4560 works with the same motherboards/RAM as the i3-7100.
Do you know which specific i5 model you had in your old PC? Unless it's a pretty old model, you're probably not going too see much if any performance improvement with the i3-7100 (might even perform worse in some cases).