orbitals - How to rationalise with MO theory that CO is a two-electron donor through carbon?

A question I am looking at is as follows:

$\ce{CO}$ is isoelectronic with $\ce{N2}$. Sketch MO diagrams for $\ce{CO}$ and $\ce{N2}$. Point out key differences between the diagrams and use the diagram to explain why $\ce{CO}$ acts as a two-electron donor through carbon rather than through oxygen.

Understandably, the key difference between these molecules is that $\ce{CO}$ is heteronuclear, and thus will have differences in energy between the molecular orbital and the atoms.

But I can't explain why $\ce{CO}$ is a two-electron donor using MO theory, even though I can with Lewis?

Does anyone have any thoughts?

In the above MO diagram, the 5σ is the HOMO. But it is closest in energy to oxygen's 2p orbitals, so why is it centered on carbon?