When you hike in the high altitude (5,000 to 11,500 feet (1,524 to 3,505.2 m) above sea level), your body has to work harder. At higher altitudes, the air is thinner. There is less available oxygen and it becomes more difficult to breathe.
However, the level of sensitivity to the high altitude is different from individual to individual so you might find it difficult to breathe sooner than your friend who is hiking with you, for example. I personally did not feel the high altitude until I reached 8,000 feet. That was Mt Waterman hike back in 2016. Now it doesn’t bother me as I became acclimated to the altitude. Also, it can be different for you on different days depending on your physical condition.
Dogs seem to handle the high altitude better than humans generally but they do get tired sooner than if you were hiking in the lower altitude. Here is Xena power napping at a peak. It’s important to listen to your body.