how is that the reminder of 5 power 99 divided by 13 is 8? and why not 5?

Here we express 5⁹⁹ binomially as follows

5⁹⁹ = 5*5⁹⁸ = 5*25⁴⁹ = 5* (26 - 1)⁴⁹

Now (26 - 1)⁴⁹ = C(49,0) * 26⁴⁹ +  C(49,1) * 26⁴⁸ 1¹ + C(49,2) * 26⁴⁷1² + ...+C(49,49) * 1⁴⁹  

Here all terms except last are divisible by 26

Thus we may write it as

(26 - 1)⁴⁹ = 26n - 1  (where n is some positive integer)

Thus,

5⁹⁹ = 5* (26 - 1)⁴⁹ = 5* (26n - 1) =  130n - 5 = (term divisible by 13 - 5)

Thus when this expression is divided by 13 we obtain remainder  = 13-5 = 8