Ta có:
$(x-5)^{x+3}$ - $(x-5)^{x+13}$ = 0
<=> $(x-5)^{x+3}$ - $(x-5)^{x+3}$ . $(x-5)^{10}$= 0
<=> $(x-5)^{x+3}$.( 1 - $(x-5)^{10}$) = 0
<=> \(\left[ \begin{array}{l}(x-5)^{x+3}=0\\1-(x-5)^{10}=0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=5\\x=6 hoặc x = 4\end{array} \right.\)
Vậy x = 5 hoặc x = 6 hoặc x = 4