Colorado Springs is about the same altitude (~6000ft), Denver is only a little lower. By and large you don't notice unless you do something that makes you breathe hard, in which case it'll take you a while to catch your breath for the first few weeks.

Honestly the biggest annoyance about living at altitude is baking recipes require adjustment pretty much all the time, you can't just use a bread recipe designed for sea level and expect it to work right.

My experience says that 6000 feet will be noticeable, but you'll be able to, say, climb a flight of stairs and be a bit more winded than usual. As another example, the Paradise visitor's center at Mount Rainier sits at (IIRC) 7K feet. Plenty of fat people waddle out of their cars and make it across the parking lot just fine. They don't generally go very far up the mountain, but they make it. And the residents of Denver, CO seem to survive at 5200 feet.

To me, "noticing altitude" starts at about 10K feet. For reference, life-long endurance athlete who still stays in pretty good shape in his middle-age.

I live in Colorado. You get used to the altitude in a few weeks.

I was in Bogota earlier this month. We flew in from sea level, and felt some degree of crappy for a few days (and a bit scared that we were suffering mosquito-borne ailments from our previous adventure before we realized the altitude).

We eventually settled in, but 8000 ft up is for real.