{[(13 x2) - 1]⁴⁹ x 5 } / 13 is our expression

now we can expand this binomailly

we find that the numerator has 50 terms, and out of them , all except the last term, which is =   1 x 5 is NOT a multiple of 13..

so the remainder is 5.

try doing all this on paper and you will see that it makes sense. reading it here may seem i little scary.

all the best