I purchased the X5. It is in amazing shape except for the fact that at certain lower speeds the transmission shudders and when driving at 35-45mph the RPM's are constantly fluctuating so I am thinking it needs a torque converter at the least

Try a fluid(valvoline max life lt71142 spec) and filter(ZF) swap with a tube or 2 of dr tranny shudder fix...

I think it was at about 80,000 miles that I replaced the chain tensioner with the redesigned version from BMW. They increased the amount of travel to keep the chain tighter longer. I don't know when that went into X5 production. I think it was in sometime in 2003.

About a year ago I purchased a timing chain kit when they went on sale. Just waiting for unusual or extended noise on startup. I now have 119,000 miles on an engine that was modded at 2,500 miles after purchase and much more along the way.

If you regularly change the tensioner the guides can last over 1/4 million miles. If you hear the rattle at start, change the tensioner before you get into guides. Of course if you can inspection scope your way in there first to confirm