The right answer apparently has all factorials having canceled each other out, but by my application of the MacLaurin series steps, I don't end up with a factorial in the denominator, only in the numerator. I get that the numerator should have one since you divide a fraction by k! so that k! ends up going into the numerator, but why does another one end up in the denominator afterward?

Question: Find the Taylor seres about the indicated center, and determine the interval of convergence.

f(x)=1/(x+5),c=0

Here's what I get:

Summation from k=0 to infinity: (1k)(xk)(k!)/5^k+1