Where are the version of 18.04 LTS prior to 5 found? We have an application that stopped working on 18.04.5 and want to install 18.04.4 and possibly earlier. They don't seem to be any links to the older versions on http://cdimage.ubuntu.com/releases/
Point releases don't work like that!
Point releases exist because LTS releases are supported for 5 years. We use point releases to consolidate updates so that people installing the release years after the initial release do not have years' worth of updates after system installation.
If you install an older point release, you will still get the same updates and will end up with the same packages as the newer point release because they are the same exact distribution.
Holding back updates is not a good plan either. Keeping up with updates is an essential maintenance task unless your device never connects to the internet. Instead of asking how to install an older point release, you should ask about the actual problem that you experience in 18.04.5. There is likely a better solution to your problem!
Old releases can be found here: https://old-releases.ubuntu.com/releases/18.04.4/
Ubuntu LTS releases offer two kernel stacks; but you've provided no specifics as to your issue thus this may not help, so rather than installing 18.04.4 which will update to 18.04.5 on first update!, one option maybe to switch to the other kernel stack (esp. if you're using the HWE stack).
You're talking about an update that occurred more than a year ago now anyway (https://fridge.ubuntu.com/2020/08/14/ubuntu-18-04-5-lts-released/ shows the ISO release date of 18.04.5, but installed systems got the update a week+ before that date) so you're missing details most probably and likely blaming the wrong thing.
Ubuntu 18.04.4 using the HWE stack used the kernel from 19.10, ie. the 5.3 kernel. The upgrade to 18.04.5 with the HWE stack caused it to upgrade to the 20.04 or 5.4 kernel.
If however you were using the GA stack, there was no change, as the GA stack remains on 5.4 and is supported the life of 18.04.
You can view https://wiki.ubuntu.com/Kernel/LTSEnablementStack for more details on the stack choices offered with Ubuntu LTS (with 18.04 the ISO used to install your system controlled the default stack; 18.04 & 18.04.1 media defaulted to GA, later media defaulted to HWE). If you want to use the GA stack instead of HWE; search for "To downgrade from HWE/OEM to GA kernel:"