May and early June may be too early, depending on how hard the previous winter was. On our last trip we reached the Alaska state line on June 1st and some of the campgrounds and attractions were still closed. I think they usually say the season starts about June 15th but someone else may say differently. In any case, there aren't all that many roads. Summer is when Alaska DOT repairs roads so you're bound to have some delays and hit some bad patches where you'll have to slow down quite a bit. I guess it's safe to say that one doesn't go to Alaska if they want to drive full speed ahead and do it all in a couple of weeks. It's just too big for that, plus construction delays, plus "frost heaves" that can make you bottom out and be airborne if you're going so fast you don't see it. In other words, the pace is slower there. But it's really a neat state to visit so enjoy your trip.
ArdraF