If I understand your question correctly, you have installed 2 SW2013 versions (SP4 and SP5)?
Why?
If this is the case, it is really not advisable (registry database, solidworks data, drilling database etc...).
In a pinch, it is tolerated 2 major versions, e.g. SW2013 in production and SW2014 for testing but duplicating the data for testing so as not to damage your files.
the installation of SP05 must be done in the form of an update of SP04.
As jmsavoyat says, you can install two different versions on the same workstation (2013 and 2014 for example) but having for each version a "SolidWorks Data 2013" folder and another "SolidWorks Data 2014" folder.
Yes, I am in a single position (one-man band, employee, boss, draftsman, after-sales service, secretary, sweeper, etc...)
I just tilted that the toolbox is normally compatible with any version, if I'm not mistaken, it would only be steps. On the other hand, in Data there are a large number of parameters related to the version.
I'm going to check a small point on the path of the settings (placed on another physical ssd disk) that the maintenance had created for the drawings etc.