Update from 3.6.x to 3.6.5 Timeout
From Joomla! Documentation
Timeout problems if you update.
This pertains only to Joomla! version(s): 3.6.x
What is the cause
As we have implemented a reinstall feature in 3.6.0 we always need the complete (bigger) `Joomla_3.6.x-Stable-Update_Package.zip` (10Mb) package on the update server. With some servers this may result in timeouts on updating / downloading the update package.
How to fix
If you have such a site please use the table below to find the correct package.
Note: This workaround is only valid for upgrades within a minor series (i.e. 3.6.x to 3.6.5). For upgrades between minor series (i.e. 3.5 to 3.6 or 3.6 to 3.7) the update package is always used. If you are experiencing issues updating using the larger packages, you should contact your hosting provider to have your settings updated. As of December 18, 2016, the update package for the upcoming 3.7 release is nearly 11Mb.
There is a PR to differ between a update and a reinstall: https://github.com/joomla/joomla-cms/pull/11497 as long as this is not merged we need to use this workaround on sites that time out when using the full package.