Let a be the first term of the AP and d be the common difference (i.e.
difference between any 2 consecutive terms)

nth term of an AP is given by a + (n - 1)*d

5th term = a + 4*d = 12 --- (1)
10th term = a + 9*d = 27 --- (2)

Subtracting 1st equation from 2nd, we get
5*d = 15 or d = 3

Substituting for d in (1), we get a + 4*3 = 12, or a = 0.

So the 1st term of the AP is 0, and common difference is 3.

15th term = a + 14*d = 0 + 14*3 = 

Hope this helps :)