I got (x-3)(x^2+9) is it right?

Fantastic !  It's not an easy problem.  I'm not even going to go into a whole big presentation of how to do it.  I'll just simply answer the question you asked:                                 Yes! Your answer is correct.Great work !

[tex]\frac{x^5-81x}{x^2+3x}=\\
\frac{x(x^4-81)}{x(x+3)}=\\
\frac{x^4-81}{x+3}=\\
\frac{(x^2-9)(x^2+9)}{x+3}=\\
\frac{(x-3)(x+3)(x^2+9)}{x+3}=\\
(x-3)(x^2+9)[/tex]