Solving an Inequality to Determine profit margin

[PhysicsAdvice]

Revenue Equation: R(x)=-x^2+10x Cost Equation: C(x)= 4X+5
Average profit= profit equation, P(x)/x

therefore p(x)= R(x)-C(x)=-x^2+6x-5

(-x^2+6x-5)/x=(-1(x-5)(x-1))/x, I then found that x is positive between 1 and 5, therefore average profit is positive in that range, however, the answer is if x>5, where did I go wrong?

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[Dick]

I don't see you've done anything wrong so far. You gave the answer. But what is the question??

 

[PhysicsAdvice]

simply, what values of x will produce a positive average profit? I have gotten three questions which I believe to be right wrong in a row now, I believe the answers are off :)

 

[Dick]

simply, what values of x will produce a positive average profit? I have gotten three questions which I believe to be right wrong in a row now, I believe the answers are off :)

They must be. At x=6 I get R=24 and C=29. That doesn't look profitable to me.