Congratulations on the purchase!
I'm not at all familiar with the M5 gearing, so my answer is going to be somewhat broad. To maximize your fuel economy, you should drive in the highest gear that you can without lugging the engine. For my X3, that 'cross-over point' is at about 2,000 RPM; if I let the revs slip below that mark, the engine isn't really happy, and I really should be in a lower gear... For something with a high-torque V8 (like your M5 or a C5 Corvette) the 'cross-over point' is a bit lower.
In your specific example of 100-120 km/h (~60-75 mph), I would think 6th gear is best for cruising; that's why BMW gave it to you. At 100 km/h (60 mph), you might have to downshift to 5th to accelerate (say, for a quick pass), but at 120 hm/h (75 mph), I think you'll be able to pull even in 6th gear. To give a specific point of reference, my 6-speed C5 will run very happily at 75 mph in 6th gear and ~1,600 RPM. And it will accelerate well there too. But down at 60 mph, if I don't drop it into 5th, the acceleration is noticeably more anemic (even though I'm almost -- but not quite -- lugging the engine).
Another 'rule-of-thumb' I tend to use (and this is based solely on my own observations), is that most engine-transmission combinations seem to be happy cruising in a gear that's equivalent to your speed (in mph) divided by 10, plus 1. For example, at 30 mph, you should be in 4th gear (30/10 = 3 + 1 = 4).
X3 w/6-speed & Sport Package:
A sports sedan disguised as an SUV...