If the 1st and 6th terms of an A.P are respectively 5 and 15 the sum of the first six terms is

5d = 15-5 = 10, so d=2

S6 = 10/2 (2a+5d)
Now just plug and chug

or,

sum of n terms = (n/2)(first + nth term)
= 3(5+15) = 60

btw, oobleck meant to say:
S6 = 6/2 (2a + 5d)