Answer
$(y+5)(y-5)^{2}$
Work Step by Step
Step 1. Factor both denominators.
The first one is a difference of squares,
the second is is a square of a difference.
$\left\{\begin{array}{lll}
y^{2}-25 & =y^{2}-5^{2} & =(y+5)(y-5)\\
y^{2}-10y+25 & =y^{2}-2(y)(5)+5^{5} & =(y-5)^{2}
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=(y+5),(y-5),...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
One of the two factors $(y-5)$ is in the list, we add the other one to the list
$List=(y+5),(y-5),(y-5),...$
Step 4. LCD is the product of the listed factors.
$LCD=(y+5)(y-5)(y-5)$
or
$(y+5)(y-5)^{2}$
