You have a transom rot issue, and you will need to have it fixed before I would use the boat again. Those holes should have been epoxied over, 5200 is fine unless it breaks down or the holes get bigger, but is really better suited in sealing a screw, not the entire screw hole. Although the 5200 is not the right way to fix that in the first place, it's properties should have kept that sealed, maybe they used a silicone sealant, if it came out without much work it was not 5200.
You have several choices, you can have the boat brough to a fiberglass repair shop, have the engine removed, drive unit taken off and have the interior of the transom cut out, remove the wood, have them replace it with new wood(marine grade treated wood)...wood that was coated in epoxy before being bonded to the hull, and then refiberglass over the wood. Having the transom replaced is the ONLY thing I recommend, but it will cost the most. It will also give you the safest fix and the one that wil last the longest. There is NOTHING wrong with wood in a transom, it is cheap and lasts if cared for, just in your instance the previous owner did not care for it correctly.
Your other option is to drill several small holes in the transom and let it drain and then pump in resin, but if the wood has substancial rot, you will loose a lot of its strength, yes you will harden up soft spots but it will not take a load like it used to.
Some guys have used git rot to fix rotted wood, but I would NOT use this for a transom, for a deck maybe(although I always recommend doing the job right instead of cutting corners), but not for a transom. Git Rot will solidify what it can reach but will not bring back the strength of the transom like a sheet of wood will. It will ge trid fo f aosft spot and bring back some of the strength, but not enough to support the forces from your outdrive which pushes the boat.
I would also recommend having your stringers near the transom checked, they might have had water seep in depending on how bad the transom itself is, and how well Grady sealed the transom to hull connection, it should be good but is surely worth being checked to be safe.
If you wish to save money, disconnect all of the wiring to the engine yourself and mark them well, if you have access to an engine hoist, removing it yourself as well will save you even more money. Even if you pay a friend to help you it should be a lot cheaper to remove the engine then having the yard or repair shop do it, they will charge an arm and leg. Giving them a boat with the engine removed will get you in and out faster as well.
Sorry for the bad news, but there is only one way to fix that problem and keep you and your crew safe. Hopefully it all works out for the best.