What's the highest altitude that you ever saw a bird swoop past your plane?

The other day I was flying at 5000' MSL, over land that was mostly about
1000' (so 4000' AGL) and saw a flock of birds, hawks of some sort I think,
one of which came close enough to make me quite nervous (although from the
way he was flapping I think he was much more nervous than I was).

I don't think I've ever seen birds above 3000' MSL / 2500' AGL or so before
and I was pretty surprised...

Do birds typically stay low, or have I just been lucky until now?