I have Magento v1.7.0.2, 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?