With this question

suppose p and q both represent prime numbers such that

5 x p + 7 x q= 109
find the value of the prime p.

on rearranging,

now, 109-7q should be a multiple of 5,

and for that, 7q must end with 9 or 4 as unit digit.

as q is prime,

let's try q=2,

(109-7×2)/5=95/5=19

which is a prime.

hence, P=19 and Q=2

we got lucky.