jmc

Recall that for positive integers $a$ and $b$ $x^a{x}^b=x^{a+b}$. Thus, if $h(x)$, $f(x)$, and $g(x)$ are polynomials such that $h(x)=f(x)\cdot g(x)$ and if $x^a$ and $x^b$ are the highest degree terms of $f(x)$ and $g(x)$ then the highest degree term of $h(x)$ will be $x^{a+b}$. In our case $f(x)=x^2-7x+10$, the highest degree term is $x^2$ and $h(x)$ has highest degree term $x^5$. Thus, solving for $b$ in the equation $x^5=x^2{x}^b=x^{2+b}$, we find $b=\boxed{3}$.