Correct. Use FOIL.

$\displaystyle{\left({2}+{i}\right)}{\left({5}+{i}\right)}={2}{\left({5}\right)}+{2}{\left({i}\right)}+{i}{\left({5}\right)}+{i}{\left({i}\right)}={10}+{2}{i}+{5}{i}+{{i}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle={10}+{7}{i}+{\left(-{1}\right)}={9}+{7}{i}\usepackage{cmbright}\Huge\$

The real part is 9.