The number of unpaired electrons in ${\text{Fe}}^{3+}$ ion are

The atomic number of iron (Fe) is  Z = 26

Electronic configuration of iron, $\text{Fe}\to 1{\text{s}}^{2}2{\text{s}}^{2}2{\text{p}}^{6}3{\text{s}}^{2}3{\text{p}}^{6}4{\text{s}}^{2}3{\text{d}}^6$

When iron loses three electrons then  ${\text{Fe}}^{+}$  ion is formed.

Electronic configuration of  ${\text{Fe}}^{+3}\to 1{\text{s}}^{2}2{\text{s}}^{2}2{\text{p}}^{6}3{\text{s}}^{2}3{\text{p}}^{6}3{\text{d}}^5$

There are total 5 unpaired electrons present in  ${\text{Fe}}^{3+}$ ion.