I have a 2001 5hp 4 stroke. I am replacing the prop, prop holder, seal and bearing. I noticed a shim between the bearing and holder housing. On the parts breakout 2 sizes were shown. .10mm and .15mm. How do you determine which one or how many to use.

If you are just replacing those parts, you *should* be okay to use your old shim provided it's in good shape. I haven't looked at a BF5 manual, but the shop manuals for other ones have a cryptic way of determining what shim to use, usually there is a set of Japanese characters scribed or marked somewhere in the gearcase and per the table in the manual that dictates which shim thickness to use...
Now that I have confused you, I would just try using your old one. To double check, you could check the thickness of the new parts you're putting in that ride against the shim and if they're the same as the old ones you're replacing, I'd say stick with the same shim. Good luck.