If you are running 10.6.8, you have at least an Early 2006 iMac (but not earlier because that would make it a G5 which renders this whole thing moot). It also can't be any later than a Late-2009 since that was the last model that could support 10.6.x
If it's a 2006, you are pretty much dead in the water so to speak and it's time to buy a new iMac because the most you are going to upgrade to is 10.7.5
So, I am going on the assumption that you have a 2007 or later iMac....
You are right on the cusp of being able to upgrade to macOS Sierra if you have a 2009 (macOS Sierra How to Upgrade). However, I don't recommend you going that far. In my personal experience, the problems associated with Sierra have far outweighed any potential benefits I never needed in the first place so I advise skipping or waiting out this version.
Regardless, you must upgrade to El Capitan first; just stay here for now.
As for CS5, there's not too many known issues, but generally it appears that it works. Though CS5 is 7 years old, so, it's highly unlikely you will find very much way in the development of "fixes" for any outstanding issues.
Happy to update to not the latest OS, but just enough to make sure I can access the web (already can't do Linkedin). What should I do? Thanks!
Since your particular iMac (assumed) is capable of running El Capitan, I would suggest only a couple of hardware upgrades:
- Max out memory (depending on your model, this can go from 6GB to 32GB)
- Add an SSD (I personally use and recommend the Samsung 850 EVO; I use it in my iMac)
- Do a full Time Machine backup and do a fresh clean install (preferably on the new SSD) to ensure you are starting from "factory."
ifixit.com has an excellent guide for opening your machine (the 2007 - 2011 iMac's used magnets to hold the display in so removal is actually fairly easy)
Bottom Line: As long as your iMac is at least from 2007 onward, you have a bit more life that can be extracted from your machine as it supports at least El Capitan. A few dollars spent on upgrading your hardware will speed things up and breathe new life into it.