Fresh deer meat at room temprature still ok?

I bought 40kg of deer from professional hunter. He kept it in cold storage for 2 days after he shot it, then we cut it into small parts together in cold room. Then I took it to my home to put it into vacum bags and to freezer.

Anyway my vacum machine broke and it took 3 hours to fix it. All together the meat was at room temprature for 5 hours before I put it into freezer. I am reading that the safe limit is 2 hours. Is that "rule" also for fresh deer meat that was shot 2 days ago and never frozen before?