The square of a binomial is:
(a + b)² = a² + 2ab + b²
The expression is
m² + 10m + __
which means that
a = m
and
2ab = 10m
ab = 5m
Replacing with a = m,
mb = 5m
b = 5
Then the factored expression is:
(m + 5)²
and the perfect square trinomial is:
(m + 5)² = m² + 2(5)m + 5² = m² + 10m + 25
