Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 5; b = 13; c = 8

= 5.8 = 40

And either of their sum or difference = b

= 13

Thus the two terms are 5 and 8

Sum = 5 + 8 = 13

Product = 5.8 = 40

Hence the roots of equation are