DIY:
Turbines require a lot more engineering than "fins on a disk" as they're sculped, angled, and tapered causing the air to be drawn in, compressed, and pushed into the engine. This requires tremendous impeller speed, a very good balance, and very tight clearances. The impellers of turbochargers and superchargers often reach into the 80k-100k RPM range.
Can you machine something that precise?
Junkyard Style:
I'll put forth some monkey math to help you sizing junkyard turbos for your lawnmower engine then follow with an example.
(donor CID) x (donor redline) x (qty donor turbo) = (dest CID) x (dest redline) x (qty dest turbo)
The smallest turbocharged car engine I've seen is a 1 liter suzuki / chevy sprint, and 1 liter equates 61 cid. A typical 5 HP briggs has 11.57 cid of displacement.
61 cid x 6000 rpm x ? = 11.57 cid x 3600 rpm x 1
36600 x ? = 41652
? = .1138
The .1138 means a 5 HP briggs can drive .1138 turbochargers as found on a 3 cyl, 1 liter chevy sprint/suzuki samarai engine.
Another way of looking at it is you'd need quantity NINE 5 hp briggs to drive that turbo to it's maximum boost.
The output of most turbochargers is not linear, so if you drive one with 1/10th the cfm you will get quite a bit less than 1/10th the power out of it in the end.