I took Eric and Eric's insulin vial — which was nearing the end of its 28-day lifespan — on a trip to Pennsylvania. We traveled by car 7 hours, with the insulin in a small insulated lunchbox that had a coldpack on the bottom (below the insulin) and another above it. The insulin was still plenty cold when we reached our destination, and the cold packs were only slightly thawed. We had brought two spare cold packs with us and we tossed those in the freezer as soon as we got there, and left the vial in the lunchbox with the packs we'd had in there in the first place. By morning, the packs were noticeably softer but still very cold, and the insulin vial was still cold too. We swapped out the cold packs for the frozen ones, put the thawed ones in the freezer, and stuck the lunchbox in a corner away from windows/sunlight before going about our day. Did this routine 3 days running and had no loss of potency at all. By the time we got home, the vial we'd taken with us was in its last day of "official" potency so we threw it out and opened a new one the next day.
Now, this WAS Pennsylvania, and it was nowhere near as hot as, say, Florida or Arizona would've been. But it was still plenty hot, 80 to 90 degrees each day, albeit cooler at night. I would imagine that your 5-hour trip would be okay using the same routine, particularly if you were using a freshly opened vial. Insulin can be unstable at high heat, it's true, but if you take steps to keep it cool, it will be fine for a couple of days. I'm not sure I would have wanted to be away any longer than I was, knowing that the vial had already been open for 3 weeks,