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According to molecular orbital theory, the total number of bonding electron pairs in $\mathrm{O}_2$ is
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$5$
The molecular orbital electronic configuration of $\mathrm{O}_2$ is
$\begin{aligned} & \mathrm{O}_2\left(8+8=16 e^{-}\right)=\sigma 1 s^2, \sigma 1 s^2, \sigma 2 s^2, \sigma^* 2 s^2, \\ & \sigma 2 p_z^2, \pi 2 p_x^2, \approx \pi 2 p_y^2, \stackrel{*}{\pi} 2 p_x^1 \approx \stackrel{*}{\pi} 2 p_y^1 \\ & \end{aligned}$
(Unstarred $\sigma$ and $\pi$ represent bonding orbitals.)
$\therefore$ number of bonding electrons $=10$
and number of bonding electron pairs $=5$
$\begin{aligned} & \mathrm{O}_2\left(8+8=16 e^{-}\right)=\sigma 1 s^2, \sigma 1 s^2, \sigma 2 s^2, \sigma^* 2 s^2, \\ & \sigma 2 p_z^2, \pi 2 p_x^2, \approx \pi 2 p_y^2, \stackrel{*}{\pi} 2 p_x^1 \approx \stackrel{*}{\pi} 2 p_y^1 \\ & \end{aligned}$
(Unstarred $\sigma$ and $\pi$ represent bonding orbitals.)
$\therefore$ number of bonding electrons $=10$
and number of bonding electron pairs $=5$
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