Considering a used E53 X5

[Booki]

Shopping around for a used E53 X5 with the diesel, 04 models upwards.

I have noticed on the models I have driven (all auto's), when going wide open throttle the transmission revs out quite a bit then has a bit of a delay/slip when changing up gears.

Is this normal?

Every X5 I have driven so far has done this, with issues on most forums about the transmission on X5's ( 6 speed auto ZF) it has me wondering.

Do they normally shift like this? or do these transmissions not have much life left in them?

They seem to shift fine when manually selecting gears.

Are there other things I should be aware of when shopping around for a used E53?

I have also found not a whole lot of information about the diesels for the X5 - can't seem to find any workshop manuals or servicing guidelines anywhere I look other then this - BMW Workshop Manuals Which is clunky and hard to read