There's not a whole lot to eat at high altitude. Wild yaks are probably representative of the limits of grazing animals in the Himalaya, and can be found between about 3000m and 5500m. You can find domestic yak a little way below this, but not much further as their adaptations to cold weather and high altitude make lower altitudes unpleasant for them. They like ambient temperatures no higher than 15 degrees.
Snow leopards are probably representative of predator species, and can be found over a slightly larger altitude range... perhaps 2700m to 6000m in summer, but like yaks they prefer to live above the tree line. Unlike yaks they do sometimes visit lower altitude, as low as 1200m in winter when they move down into the forests when the weather makes higher altitudes uninhabitable.
Clearly an active mammal can live at very high altitudes, even though the effective oxygen percentage up there is about ten percent (presumably thet number was generated from the actual partial pressue or O2 up there, but I don't have those figures or the conversion formula to hand). The issue is not so much surviving up there as thriving... it is easy to burn a lot of calories staying warm and moving around on steep, broken mountainsides, so I doubt many things will be staying up as far as 5-6000m for extended periods of time.
I don't think there's much scope for omnivory that far up. You either graze or browse on comparatively low quality plants, or you eat the things that do. I suspect you have to drop down to well below the treeline to make it practical to live omnivorously. The altitude of the Himalayan treeline varies considerably (ranging from 3200-4900m), so I'd expect your yetis to be mostly found below 3000m unless they're largely predatory for at least part of the year, or they're grazing animals which seems unlikely given your description.