Mate I have the same drama. Getting mine back today from the shop after a water pump and alternator install. Mine happens up around the 110 km/h (70 mph).

In my eyes new tyres shouldn't make a difference, not on an X5 anyway, as you have not changed the rolling circumference etc like on a 4wd with over size tyres.

On other cars (I haven't checked the X5), a lower control arm change is an easy DIY job.

Some others on here will be all over it I'm sure.