To find the least common multiple of x^2-25 and x-5, we need to factor both expressions first.
x^2-25 can be factored as (x+5)(x-5)
x-5 is already factored.
Now, we can find the least common multiple by taking the product of the highest powers of each factor.
The highest power of (x+5) is 1, and the highest power of (x-5) is 2. Therefore, the least common multiple is:
(x+5)(x-5)^2
which can also be written as:
(x-5)(x^2-10x+25)