There's really no way to tell, but as a 34-year-old who's run really inconsistently for the past 10 years, it's not at all unrealistic for a somewhat athletic but otherwise untrained male to hit a 5-minute mile with a year or so of consistent effort.
But it depends tremendously on (a) what kind of shape you're in now, (b) how your body responds to training, (c) how much you can realistically commit to training, (d) how long it takes you to recover from workouts, (e) your propensity for injury, and so on.
Do not try to wing this. FWIW I think running all-out 400s without any base work beforehand is a risky proposition at our age. Run all easy miles for a couple months. Get yourself on a structured program. I like Daniels stuff, adapted to account for the fact that I'm old and somewhat injury-prone. A huge thing for me (and a lot of 30-somethings) is that recovery time goes way up, as does propensity for injury. So take recovery seriously, and don't push your workouts too much. Remember the law of diminishing returns, and that you need to be able to get up again run again the next day.
Side note for people over about 30: As Outside itself has noted, protein requirements for athletes in their 30s are actually kind of massive: anywhere from 1.2-1.7 g per kilogram of body weight is the best estimate right now, from what I've seen. That's 80-115g of protein per day for a 150 lb athlete, which actually requires a lot of effort to get. But once I took that into account, I really do notice that I recover faster from hard workouts. Just a little tip for ya if you wanna get serious about training at such an "advanced age."