I have Magento v22.214.171.124, and I tried it on www.magereport.com. The produced report shows that I missing the patch 8788, while 5344 is reported as unknown. I have recently installed the patch 8788, and the installation was successful. I also checked the file /app/etc/applied.patches.list and the patch SUPEE-8788 is mentioned there.
As for the patch 5344, when I downloaded it from https://www.magentocommerce.com/download, I received a patch file containing the name 5345. I also checked the file /app/etc/applied.patches.list, and it mentions SUPEE-5345, as well.
Is there any other problem with these very patches, or Magereport may miss information depending on the Magento installation?
Magereport does not have access to your site's code. It may also miss to generate a accurate report.
I have faced similar issue with the sites I work on.
I get following message for some of the patches.
We were unable to conclusively check your shop. The check might have been blocked by other emergency measures you, or your provider, have taken.