Answer
$$3x^4+5x^3+x-10$$
Work Step by Step
Like terms must (1) be raised to the same power and (2) consist of the same variable (i.e. x and y are not like terms). It is also important to note that numbers are all like terms with each other when not multiplied by anything. Thus, combining like terms, we obtain:
$$ \left(3x^4-2x^2+x-7\right)+\left(5x^3+2x^2-3\right) \\ 3x^4+5x^3-2x^2+2x^2+x-7-3\\ 3x^4+5x^3+x-10$$
