Answer
True.
Work Step by Step
If the trinomial $ax^{2}+bx+c$ can be factored, it will be in the form $(x+n)(x+m)$, where
the product of integers n and m is $c$
their sum is $b.$
Do we have a pair of factors of $-24$ with sum of $+5?$
... Yes, they are $+8$ and $-3.$
The trinomial factors to $(y+8)(y-3)$, so
the statement is true.