Is it Right? Evaluate the limit, if it exists : lim x-->infinity (5^x-3x)/(e^x+5x^2)?

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Is it Right? Evaluate the limit, if it exists : lim x-->infinity (5^x-3x)/(e^x+5x^2)?

Evaluate the limit, if it exists : lim x-->infinity (5^x-3x)/(e^x+5x^2)

lim x-->infinity (5^x-3x)/(e^x+5x^2) => Infinity/Infinity

Since it is infinity/infinity , we can use L'Hospital's rule.

So:
lim x-->infinity (5x*ln5-3)/(e^x+10x) => Infinity/Infinity

Since it is infinity/infinity , we can use L'Hospital's rule again.

So:
lim x-->infinity 5/(e^x-10) = 5/infinity = 0

I just need to know if I did any mistakes.. if so.. please correct me..

Thank You!