I used cocaine probably three times about 4-5 months ago. Will I pass a hair follicle if they take my underarm hair?

How much cocaine, what was its strength, what are the acceptable limits on the test.

Is the test an employment test, one for probation, one for family services ?

But if it was minor usage, and that long ago, while residue may show, it should pass on most tests

It's an employment test and probably used a gram all together over a month long period about 4 months ago

A hair drug test is meant to show consistent use over time. Even-though a drug can show up in body hair anywhere from 9-12 months back it sounds like you didn't do enough to worry about.