BB sizing
 

I have a crankset that was originally on a shimano square taper 68mm-113mm bottom bracket. I would like to use this crankset on a new frame whose bb shell is 73mm. My question is, should the new bottom bracket be a 73mm-113mm or a 73mm-118mm? I don't quite understand where the extra 5mm will go, just the shell, or the spindle length too. Thank you

The new spindle length will depend on what bike the crank came off and what it's going on to. You want the chainline to be correct for the new bike. If you are swapping it from one road bike to another (unlikely given the 73mm shell dimension), no change in spindle length should be needed. Same applies for MTB to MTB. If it's going from a road bike to a MTB, you'll want to account for the difference in chainline which will be between 2.5 and 5mm according to Sheldon Brown.

Assuming you want to move the crank outwards by 2.5mm, you'll need a spindle that's 2.5mm longer on the drive side. According to what I've read (I need to measure for myself some day), most square taper bottom brackets are asymmetrical. Assuming that's the case, you'll want a 115mm BB to get close to the ideal chainline. If the bike has a larger diameter seat tube (aluminum frame), you'll probably want to go with a 118mm BB to move the chainline out a full 5mm.