How to install 10.11.4?

if you don't already have 10.11.4 in your possession right now in some installer package it is not available to download from Apple any longer.

you're only option is 10.11.5 from the app store.

if you can use that, download the installer package from the App Store, run the installer from

Macintosh HD:Applications/

select blank hard dirve

you should backup everything before proceeding

Use Time Machine to back up or restore your Mac - Apple Support

I have a very hard time believing that any software would only be qualified for 10.11.4 and not run on 10.11.5.

Please provide the name of this software package.

Apple doesn't work that way, and Avid should know it by now. When Apple ships a new point release, the older point releases are no longer available. Not even to users that previously downloaded the point release.

For major releases, since Mavericks (10.9), when a new Major release is shipped, ONLY users that have previously downloaded the older release will have it accessible in their App Store -> Purchases tab. Customers that have never downloaded the Mavericks or Yosemite release can no longer get it.

like I said if you don't have 10.11.4 on you, you own it, it's on file on your computer or flash drive or cloud you can no longer legally obtain it.
This is apple decision not mine.

not a whole lot changed from 10.11.4 to 10.11.5

you can at least try it on the other drive and if it doesn't work reach out to avid

http://www.avid.com/learn-and-support/contact-support

again I highly suggest you back up everything before you continue.

If that is so then you can't upgrade your Mac.