Trying to make a plugin to detect what action takes time to load

Hi everyone, thanks for taking the time to help me. Here is what I’m trying to do:

I was given the task of finding out why the wordpress of one of my friend was so slow, so I made a very simple plugin that hooks different actions and filters in order to see what takes time to load. Those are the actions/filters I hooked:

plugins_loaded, init, setup_theme, wp_loaded, wp_head, the_content, wp, wp_footer, shutdown.

And it works perfectly well, except there is a 5-6 seconds delay between wp_footer and shutdown, and I have no idea what could go in between that would slow it so much? Any actions I can hook in between those two?