I had always wondered about posted specs on horse power at such high RPMs.
The posted specs on a motor are usually peak values - peak torque, peak HP etc. The graph below shows a typical horsepower/torque plotting:

Note the peak of each curve. This signifies the maximum value reached. (Apologies to the engineers out there for the following..)
To simplify, Torque is the amount of force an engine can give, horsepower is how quick it can deliver that amount of force. (HP = Torque x RPM ÷ 5252) Thats why even though torque has dropped off, the faster RPM causes the engine to be doing more work. BUT... even spinning it faster wont make up for the torque loss at higher RPM, so HP drops off.
GEEK WARNING! Really boring stuff follows.
For maximum performance in acceleration, one wants to have each gear begin just below the torque peak, and end just after the HP peak. So, in our graph example above, if you shift into 2nd gear at ~3500 RPM, and keep it in until ~5500 RPM, you will be in the motors powerband. Ideally, shifting to 3rd would drop it to 3500 RPM again, go to 5500, then 4th drops it to 3500 etc. This gives maximum acceleration.
Ever see people race and they 'wind out' the engine in each gear? They are slower than the racer that shifts to stay in the powerband. By revving the motor to 6500 RPM they are getting LESS force than if they had shifted early. (Also, when they do shift up, and the transmission is properly set up for the powerband, they will now be above the torque curve.)
Sometimes stock transmission gears make you rev out of the powerband. In Air Cooled VW's, the transmission is set to account for heavy loads, and for highway cruising. So there is a big 'gap' between 2-3 gear in the ratio. This allows heavy loads to be pulled, but also allows for lower RPM at highway speeds. But in terms of our 'perfect' racing transmission, the gears are spaced wrong. Similar to a 5 speed transmission missing 4th.. the stock gears would be 1st, 2nd, 3rd and a 1/2, and 5th. So when shifting up, one must rev 2nd above the HP peak so when 3rd is selected it is closer to the torque peak.
Racers change the 3rd and 4th gear ratios to make them 'even' again, to maximize acceleration, and put up with the high RPM's on the freeway.
So, hope this gives a little clarity as to why they rate the HP at such a 'high' RPM, even when our use of the motor we rarely get that high.