My son turned 5 yesterday. I'm not sure how to answer you because I'm not sure what to call a "tantrum," but he occasionally (not daily) has little..."outbursts"...when things don't go his way.
So, for example, when I wouldn't let him take a particular toy to school for "show and tell" today, he crossed his arms and pouted and said, "Fine! If I can't take that toy to school then I'm not GOING to school!" He got over it within a couple of minutes, chose a different toy, and headed out the door.
At its worst, when he's angriest, he'll yell something to get a response out of us, such as, "I hate you" or "I don't ever want to see you again." Again, not daily (but probably weekly or slightly more-than-weekly), and he's over it within 5-10 minutes (by over it, I mean out of his bad mood--the actual yelling only lasts about as long as it takes to yell "I hate you" once; sometimes twice, for emphasis

).
Since you called it an "all out tantrum," I'm assuming you're describing something a bit more...tantrumy...than this. Based on what I see from other kids who are roughly my son's age (so, purely anecdotal), I'd say it's not typical for kids this age to continue to tantrum in the "screaming, kicking, flailing, crying" sense of the word, but I'm not sure at what point it becomes a developmental concern. My nephew is ~4.5, and while he has never been prone to tantrums, he cries an awful lot (probably his version of a tantrum), and my friend's son (also 4.5) gets angry and has what I would call his version of a tantrum, "Crying, yelling, refusing to talk/listen." And I would say my son is having *his* version of a tantrum when he yells unkind things or sulks.
If he seems otherwise developmentally on-track, I would probably evaluate how I was responding to his tantrums, if I were you. I would explain to him (when he's not upset) that acting that way will not accomplish what he wants, and talk about some more appropriate (and more effective, for him) ways of responding to whatever sets him off. And then I would be make sure that tantrums *weren't* an effective way of getting what he wants--refusing to give in to him because he's throwing a fit, or whatever. If he's a normal 5-year-old, he probably lacks some impulse control, but is cognitively ready to think through some better responses and to begin breaking his tantrum habit.