Verified Answer :

Alright remember, if any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0. 
k+1=0
k-5=0
Set the first factor equal to 0 and solve
k=-1
Set the next factor equal to 0 and solve
k=5
The final solution is all the values that make (k+1)(k-5)=0 true. 
k=-1, 5

Hope this helped you out :)

welshfella

when 2 items are multiplied  and the answer is 0 this means that either of them may be 0.
so we can write 
k + 1 =  0   and k - 5 = 0

- therefore k = -1 from the first and k = 5 from the second equation

so the solution set is  {-1 , 5}