smc

Let the two roots of $x^2+kx+6$ be $r$ and $s$. By Vieta's Formulas, $$r+s=-k$$ Each root of $x^2-kx+6$ is five more than each root of the original, so using Vieta's Formula again yields $$r+5+s+5=k$$ $$r+s+10=k$$ Substitute $r+s$ to get $$-k+10=k$$ $$10=2k$$ $$5=k$$ The answer is $\boxed{5}$.