2011 27" iMac After waking from sleep mode a grey screen appears, sometimes lasting 5 seconds before correct wake up screen appears. This happens about 60% of wake ups from sleep mode. I have updated my operating system to Makericks recently.

Hi Anton,

Welcome to the Support Communities!

Your post is in the Cinema Displays forum .... are you asking about an external display or the iMac itself?

OS X Mavericks updates the power button behavior on Mac computers.

OS X Mavericks: Using the power button

http://support.apple.com/kb/HT5869

Using the Power Button to Sleep & Wake

Tap the power button in Mavericks to put your Mac to sleep or to wake it up:

• Tap the power button once to put your Mac to sleep.
• Tap the power button again to wake your Mac.

Press the power button for less than a half a second to sleep or wake your Mac. This duration is similar to pressing the Space bar or Return key to wake your Mac. The power button works this way across all Macs using OS X Mavericks, including both notebook and desktop computers.

OS X Mavericks: Log out, sleep, and shut down

http://support.apple.com/kb/PH13962

If trying this new behavior does not resolve your issue, additional troubleshooting steps would be to reset the system SMC and PRAM.

Intel-based Macs: Resetting the System Management Controller (SMC)

http://support.apple.com/kb/HT3964

OS X Mavericks: Reset your computer’s PRAM

http://support.apple.com/kb/ph14222

I hope this information helps ....

Have a great day!

- Judy