Yeah it should.
A 3 bolt, 4 bolt, and 5 bolt housing, will work on a 4 bolt or 5 bolt setup.
A 4 bolt housing won't work on a three bolt setup.
Now, during the end of the manufacturing of briggs 5HPs, Briggs made the cylinder heads with 3 mounting bolt holes to work with any housing ever made.
If you want to avoid headaches, find a cylinder head with 3 mounting tabs for the flywheel shroud.