According to molecular orbital theory, the total number of bonding electron pairs in ${\mathrm{O}}_2$is

Electronic configuration of ${\mathrm{O}}_2$ is determined as follows;
${\mathrm{O}}_2:(\sigma 1 \mathrm{s}{)}^2{\left({\sigma }^{*}1 \mathrm{s}\right)}^2(\sigma 2 \mathrm{s}{)}^2{\left({\sigma }^{*}2 \mathrm{s}\right)}^2\left(\sigma 2{\mathrm{p}}_{\mathrm{z}}{)}^2\right(\pi 2{\mathrm{p}}_{\mathrm{x}}{)}^2{\left(\pi 2{\mathrm{p}}_{\mathrm{y}}\right)}^2({\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{x}}{)}^1{\left({\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{y}}\right)}^1$
Bond order $=\frac{1}{2}(10-6)=2$; double bond $\mathrm{O}=\mathrm{O}$.
The total number of bonding electron pairs is 5 as there are 10 electrons.