What are the first five terms of an = 5n - 8 show work.

It depends on how n is defined. Since n is not specified, I will. Usually these sorts of series start with 0 or 1 -- most commonly 1 so that is where I will start.

a1 = 5n - 8
a1 = 5*1 - 8
a1 = 5 - 8
a1 = -3

a2 = 5n - 8
a2 = 5*2 - 8
a2 = 10 - 8
a2 = 2 

a3 = 5n - 8
a3 = 5*3 - 8
a3 = 15 - 8
a3 = 7

a4 = 12
A5 = 17