RPM

It depends on your meaning of "BEST".
If Best means the object is to go as fast as possible and get there as quickly as you can, then 5500rpm is the number.
If Best means burning the least fuel and getting there as inexpensively as possible; That number has more variables.
This is a subjective and complicated question.

I agree with Bill.

My personal (subjective) preference for a cruise RPM, is to keep my Rotax spinning between  5100-5300 rpm. This gives me econamy, speed and low vibration/noise.

I am concerned that the engine should not be under continues load below 5100 rpm & find 5500 rpm for extended periods, just doesn't feel quite right.

I had a 912 ULS and I flew it at 4800 RPM or less, is it bad in cruise to fly it from 4000 to 4800 ? The take off was 5400 RPM.

I thought at this RPM it was too fast for the motor. My friend fly it Eurofox below 4500 RPM…

I will be interested to hear what the Rotax experts say about sustained operations at such low rpm.

My previous aircraft, ATEC Zephyr, had almost glider like capabilities, I would sometimes "loiter" at 70 knots @ about 4500 rpm, 7-8L/hr but this was not my cruising speed/rpm

TO/Climb from 5200 rpm up to 5800 rpm (5 mins) is permitted however I like to see 5750 rpm on ground role & initial climb - from then on an optimum rpm of 5450 rpm and never below 5200 rpm, to cruise altitude.

Rotax 9's are designed so as to be able to operate continuously at 5500 rpm without adverse outcomes (accelerated engine wear / overheating /etc)

I understand that Rotax 9's optimum (when the engines systems are all working at their best) continuous engine speed range, is from about 4800-5500 rpm.

I take the view that, in cruise, 5100 - 5300 rpm falls nicely between the  above.