y = -5 cos x is a basic (simple) variation of the basic trig function y = cos x.
The given y = -5 cos x could be re-written as y = -5 cos 1x.
Compare this to the most general form: y = a cos bx.
Here we see that the coefficient b equals 1.
There is a rule for finding the period of such a function: Period = 2pi/b.
Since b = 1 here, the Period here is 2pi/1, or simply 2pi.
Please stop saying "I'm terrible with math." That does not help you at all. Say, instead, "With just a little help I could understand this just fine."
