n=p^2q

n is a multiple of 5

therefore either p is a multiple 5 or q is a multiple of 5

if p is a multiple 5, p^2 will be definitely a multiple of 25
if q is a multiple of 5, q^2 will be definitely a multiple of 25

therefore, p^2* q^2 will we have at least 1 multiple of 25.

Let me know if you have any doubts.

p.pq = p^2.q =multiple of 5
it implies that wither p or pq is 5
as p ,q are primes
now.
p^q^2=(pq)^2 =25
or
p^2q^2=25q^2
in both cases it is multiple of 25