Clutch worn already?
 

1. At 5th and 6th gear around 55mph when accelerate too fast rpm will spike, and smell clutch burning.
2. The gear indicator display incorrect gear 50% of the time.

Does it mean, my clutch is done? Please help. Thanks!

1. Sounds like a worn clutch.

How many miles?... Definitely sounds like clutch is gone bro..

Sounds like a pedal adjustment issue maybe.

Absolutely not.

If the clutch pedal is adjusted so improperly that it cannot fully engage it would cause these exact issues. It's worth checking.

How many miles? I smelled a burnt clutch/rubber smell for about the first 10k miles off and on. It's fairly common on here.

If the clutch master isn't allowed to fully open/relax it will actually pump up and cause exactly that issue. Unless OP or someone messed with the adjustment, I doubt this is the issue.

OP, see if you can compress the piston further into the slave cyiinder. Doesn't take much. If you can push it a couple mm, then the clutch master cylinder is fully releasing.

Most likely, your clutch is just toast. Sorry. Bummer.

Bought it 2 years ago...now it has 27K miles on it. Daily driver. I noticed the issue #2 for about 2 months then issue #1 happened 2 days ago. I am definitely feeling loss of pressure when releasing the clutch and issue #1 becomes more often too.

Shot in the dark: Potentially an issue with the master cylinder or there is air in the line. Try to bleed the clutch first and see if it improves. You could also try to diagnose if there is a possibility of it being the master, and replace that if you are confident.

Check that you have hydraulic fluid in the reservoir for the clutch and see if it looks like air might have been sucked in.

This could be the root cause for an otherwise toast clutch.

No, if there was air in the line OP wouldn't be able to shift into gear.

Replace clutch.

I am taking it to the dealer on Wednesday and hopefully i don't have to replace the clutch.

My friend had a master cylinder go out on his '05 GTO. The symptoms were a soft clutch similar to what OP described. We bled the lines and he was able to shift a little better, but it still didn't disengage the clutch fully, but enough to get it to the shop. He replaced the master cylinder and it fixed his problem.

A clutch going out at 27k miles is a clear indication of some other problem. Driver or mechanical. He may need to replace the clutch. But if he doesn't find the underlying problem, he may encounter this again in the future.

Yes, but did the clutch in your friend's GTO slip on throttle in top gear? OP's clutch disengages just fine. It slips.

And the pedal feels soft because the clutch disc is worn down to the rivets - loose pressure plate.