Why you only need to test with 5 users

by Nielsen

0 users = 0 data
1 user = 1/3 of all problems
2 users = some more
3 users = a little less more

and so on, with diminishing returns.

This is because each additional user finds some of the same stuff as the users before them. Five users find 85% of problems and that's good enough because you can't assume that the fixes are going to work, or that the fix isn't going to introduce new problems. So "saving" the other users for a later round of testing is a better use of usability testing.

Later testing may also uncover deeper problems, related to info architecture, task flow and user needs.

When testing distinct populations it's worth using more than five test users. In the case of two populations (e.g. children and parents) three to four per population will do. In the case of three or more populations, use three per population. Why not always use just three? Because of initial overhead of conducting the test (designing it, recruiting, scheduling).

Reasoning is solid, provided the test tasks are air-tight.