Problem involving factorials and "choosing"

Q: Using the identity nC{r-1} + nCr = {n+1}Cr. Find a value of n which satisfies the equation:

4C{n-1} + 4Cn = 5.

My attempted solution:

4C{n-1} + 4Cn = 5

5Cn = 5 (by the identity given)

{5!}/{n!(5-n)!}=5

4! = n!(5-n)!

Then i'm stuck - I can get the answer by trial and error using the fact that n is obviously between 0 and 4 and also by comparing with Pascal's triangle at the second line of work but I'm convinced that there must be a way by carrying on with the algebra.

Thanks in advance for any help and apologies for not using LATEX i did try but failed badly.