Very much dependent on age, rest and general conditioning. I went from sea level to 14K at Pikes peak in 1 day and it was quite uncomfortable. I managed, but folks who lived in Denver with lower physical fitness levels than me, did better.

I guess fitness makes a difference from what these other comments are saying. My ex-wife and I lived in Long Beach (which is obviously sea level) when we were in ROTC and pretty regularly took day trips out to San Gogornio and walked to the summit in about five hours, which is ~11,500ft. Not once did that have any noticeable effect, but we were both pretty serious runners back in the day trying to become Army officers. On the other hand, she tried to summit Aconcagua during a spring break and couldn't make it due to altitude sickness. I've never been higher than Mt. Whitney, personally.

Even if you don't feel it, the altitude still makes a difference, though. I recall doing two-a-day hell weeks at Big Bear at the end of summer cross-country training in high school and there was a 5k up there at the end of that week. We all got worse times than typical at sea level, and somewhat amusingly, I recall a high school senior from Rim of the World High School (who lived up there) getting 2nd place overall the first year I ever competed in that race, beating way more seasoned competitors just because he was used to the altitude.

It works in reverse, too. There was an officer in my Armor Basic Officer Course from Colorado who gave himself rhabdo during the two-mile test the first week we in-processed, apparently because he was so used to altitude that he hadn't quite acclimated to Fort Knox atmosphere.

I went from ~500 ft above sea level (Palm Springs) up to 8,500 feet above sea level (San Jacinto Peak) in less than an hour via the aeria tram a couple months ago and it was very noticeable, my walking speed fell by a third and I was breathing a lot harder than I usually do.