That is a little old, but not outlier-level old. Most students who get PhDs at that age do not become professors, although the reason for that is a little hard to identify. Here are two serious (possible) reasons that come to mind.
1) Maybe it's harder when you're older to deal with the stress of moving several times, possibly to extremely random geographical locations, as you make your way to a permanent job. That takes it's its toll even on people in their late 20s and early 30s, and it may get harder for older people.
2) You may encounter some agism. I don't know much about agism in mathematics (I think it's not a huge problem but maybe I just haven't seen it). My hunch is that some advisors may prefer younger students because they are more intellectually malleable, but if you shop around you will find an advisor who appreciates your background. At that point, if the advisor is impressed with you, your career will go more smoothly.
Just for some context I'm a postdoc in my late 20s.