How do I fix a broken OS X update that shows as both Available and Installed?
I'd go for the standard toolkit first...


In Disk Utility, "Verify Disk Permissions" and if necessary "Fix Disk Permissions".  Also "Verify Disk" and if necessary "Repair Disk".
Reset Home folder permissions &amp; ACLs using OnyX  - Maintenance tab/permissions, tick the box at the top then Execute.
Update to 10.10.5 [or re-apply if already updated] using the 10.10.5 combo update, not the delta from App Store