Question 304644
Is your answer {{{-24x^5-10x}}}
If so, then no you're incorrect.
The degree of x in the solution should be lower than the degree of the original polynomial you started with like in the example,
{{{x^5/x^2=x^3}}}
Use polynomial long division. 
What do you need to multiply {{{(5x+3)}}} by to get {{{10x^3}}}. 
It would be {{{2x^2}}} since {{{2x^2(5x)=10x^3}}}.
So {{{(2x^2)}}} multiplied by (5x+3) would yield {{{10x^3+6x^2}}} . 
{{{(10x^3 -34x^2 -59x -21)-(10x^3+6x^2)=-40x^2-59x-21}}}
The next factor would be {{{-8x}}} which yields {{{-40x^2-24x}}}.
Subtracting then gives,
{{{(-40x^2-59x-21)-(-40x^2-24x)=-25x-21}}}. 
Finally, the next multiplier is {{{-5}}} and {{{-5(5x+3)=-25x-15}}}
Subtracting,
{{{-25x-21-(-25x-15)=-6}}}
So then putting it all together,
{{{(10x^3 -34x^2 -59x -21)/(5x+3)=2x^2-8x-5-6/(5x+3)}}}