Since the variables and the exponents are the same, the terms are like terms. To simplify, add the coefficients.

$\displaystyle{5}{{m}}^{{2}}+{3}{{m}}^{{2}}={\left({5}+{3}\right)}{\left({{m}}^{{2}}\right)}={8}{{m}}^{{2}}\usepackage{cmbright}\Huge\$