I bought some ham from the deli the other day and forgot it in the car for about 5 hours. It was a 77 degree day. When I ran out to go get it the meat still felt cool so I threw it in the refrigerator right away. Is it still safe to eat?
This is really an issue of risk.
The USDA's recommendation is not to consume meat that has experienced more than four hours of cumulative time between 40° and 140° F. Essentially, that means that the level of risk of illness from food-borne pathogens is acceptable in that range. The government's position is that 5 hours beyond a level of risk that they are willing to expose the public to.
Also be aware that (sliced) deli meat is more prone to pathogens that a whole ham.
That said, it comes down to what level of risk you are comfortable with. Personally, I would probably eat it myself, but not serve it to others.
If in doubt, throw it out.
I think the statistics is for every hour left out of the fridge the bacteria (or whatever) multiply by two. Five hours is a long time. Especially if it was intended for sandwiches (therefore, not cooked).