I recently purchased a 2001 4.6iS. I bought it to tow my trailer and racecar around, however I've experienced some interesting things while towing. I always tow in manual mode. First, occasionally when cruising in 5th gear the engine revs will go up by 500 rpm as if it has shifted down but it still says it's in 5th gear and after a little while the RPMs drop again. The RPM change is not large enough for it to be a 4th gear change. What could this be?

Secondly, after cruising for a while and usually while going uphill or with headwind, the transmission will automatically shift into 4th in manual mode. It will not allow me to shift into 5th even if I'm going downhill afterwards. Occasionally it would even shift into 3rd, again without me doing anything. It will get stuck in the lower gear for a short while and after about 5 minutes or less give me control back to shift up.

Background info:
Trailer is an enclosed 18 foot and combined weight of trailer + car is right around 6000 lbs. X5 is bone stock expect for X-pipes in the exhaust and a Prodigy brake controller. I'll use this opportunity to say that the X5 is awesome at towing. I towed 1300 miles recently and apart from the issue above it was perfect. The self level rear end + a weight distribution hitch worked well. It felt super stable, even in ~50 mph cross winds and 65 mph cruising speed. The one and only downside was gas consumption. I barely managed 10 mpg on the first half going 55-60mph and 8.7 on the return trip at 65-70mph.