Integration on an (Integration on a Limit)

If

$\displaystyle \int_1^5 \int_1^x \lim_{z \rightarrow y} \frac{z^5+z^4}{z^3+1} \mathrm {d}x \mathrm {d}y$

is equivalent to $(A \times \tan^{-1}(B) + C\pi + D \times \ln (E) + F)(\frac {x-G}{H})$ , find the value of the digit sum of $A^2 + B^2 + C^2 + D^2 + E^2 + F^2 + G^2 + H^2$ , where $A,B,C,D,E,F,G,H$ are integers.