If this exact question is repeatedly deleted, it's probably because of the ambiguity of the given equation. I see two likely interpretations, for instance:
[tex]\dfrac{(5\times5)^k}{5^{-8}} = 5^3[/tex]
or
[tex]\dfrac{5\times 5^k}{5^{-8}} = 5^3[/tex]
If the first one is what you intended, then
[tex]\dfrac{(5\times5)^k}{5^{-8}} = \dfrac{(5^2)^k}{5^{-8}} = \dfrac{5^{2k}}{5^{-8}} = 5^{2k-(-8)} = 5^{2k+8} = 5^3[/tex]
and it follows that
2k + 8 = 3 ==> 2k = -5 ==> k = -5/2
If you meant the second one, then
[tex]\dfrac{5\times 5^k}{5^{-8}} = \dfrac{5^1\times5^k}{5^{-8}} = \dfrac{5^{k+1}}{5^{-8}} = 5^{k+1-(-8)} = 5^{k+9} = 5^3[/tex]
which would give
k + 9 = 3 ==> k = -6
And for all I know, you might have meant some other alternative... When you can, you should include a picture of your problem.
