modular arithmetic - How to calculate $5^{2003}$ mod $13$

How to calculate $5^{2003}$ mod $13$

using fermats little theorem

5^13-1 1 mod 13

(5^12)^166+11 mod 13

a+b modn=(a modn + b modn) modn

(1+11mod13)mod13

12 mod 13 = 12

why answer is 8 ?

how do we calculate this

thanks