Is it normal for there to be a 5min+ period of high CPU usage when going to sleep under El Capitan?
Is it normal? No. Not with an optimal install, optimal hardware &amp; configuration. 
Is your computer stock or have you installed non-oem parts? Age can also be a factor as the thermal grease can deteriorate over time especially when a cpu gets overheated. Also Apple had indicated that you need a minimum of 1GB free to even be able to run effectively. My experience is that having much more than 1GB allows the system to run best.

What can you do to fix it? Take a free disk and install the OS on it. Boot from that disk and see if the problem disappears. If it is gone then it's a software issue. If it still exists, you have a hardware or resource issue. If it's software you can create a new user and log in under that account. If the problem is gone then it's the old user account. If it's not, do a clean install of the system. If the problem is gone then it was a problem with the system.

What can you do to mitigate it? See the second response to fix it or replace the machine.