If p and q are distinct primes and x^2 - px + q = 0 has distinct positive integral roots, then p + q has value equal to

it is got positive integral roots so roots are 1 and q as q is prime

equation is (x-1)(x-q)
= x^2 - (q+1) + q = 0

so p = q + 1

so q and q +1 are primes so q = 2 and q +1 =3 so p = 3, q = 2 and p+q = 5