Question 341388
Zeros make the numerator equal zero.
{{{x(x-1)(x-5)=0}}}
Three solutions: 
{{{x=0}}}
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{{{x-1=0}}}
{{{x=1}}}
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{{{x-5=0}}}
{{{x=5}}}
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Vertical asymptotes occur when the denominator equals zero.
{{{(x+1)(x-3)(x-4)=0}}} 
Three solutions: 
{{{x+1=0}}}
{{{x=-1}}}
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{{{x-3=0}}}
{{{x=3}}}
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{{{x-4=0}}}
{{{x=4}}}
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{{{graph(300,300,-10,10,-10,10,(x^3-6x^2+5x)/(x^3-6x^2+5x+12))}}}