a5 = 5 a's multiplied together = a*a*a*a*a
(a5)3 is a5 multiplied together 3 times = a5*a5*a5
= (a*a*a*a*a)*(a*a*a*a*a)*(a*a*a*a*a)
which is 15 a's multiplied together = a15. It is also a5*3. So you can just multiply the exponents together.
(a5)3 = a5*3 = a15