I've got 16 5.5hp air compressors. Your using the right oil. The problem is its not getting up to temp for long enough.
I assume it runs to fill the tank then shuts off right.
Mine run non stop all day. Not one has any sludge. I'm using amsoil compressor oil too though. If you can find amsoil I suggest using it.
I change the oil in my pumps yearly unless there was dirt intrusion.
Mine is a 5hp motor too, I'm sure you are right about mine not getting up to temperature. I even up one of those heaters with a magnet built in and attach to bottom of pump, Don't really notice it makes a difference. It has a large heavy pump. It's Saylor Beal 705 pump. It's really hard to get the bottom of that pump hot even in summer.
Mine are all gas powered,so even if they aren't pumping air into the tanks they are still pumping air however it just blows off into the atmosphere until the tank pressure dips enough for the valve to actuate and it pumps air into the tanks to replenish the pressure.
I used nd-30 in my pumps for years. They were impossible to start in the winter. Once I switched over to amsoil compressor oil they would start first or second pull. The oil doesn't thicken as much when cold however my operating environment is much different than yours is.
Mine are all outside,onsite.
The comment about a filter is a good idea. See if you can fit one on the oil fill or the tube that sticks out of the pumps side meant to flow air into and out of the crankcase.
I think your problem is condensation to be honest. The pump gets hot enough to create moisture but not hot enough to evaporate it,and if that's the case no syn or mineral oil is going to make any difference whatsoever.
So if you can get the nd-30 cheap go with short intervals.