Q: Display flicker on Late 2009 iMac, 21.5 inch

Hello there, Verise. 

From what your describing your iMac is experiencing flickering when you wake from sleep. The following Knowledge Base article offers some great recommendations for troubleshooting:

Apple computers: Troubleshooting issues with video on internal or external displays - Apple Support

Reset the system

You can reset the Mac's parameter RAM and SMC.

Reset the resolution

Start by resetting the Mac's parameter RAM. If the display does not come up, was previously set to an unsupported resolution, and still results in no video:

1. Start up in Safe Mode.
2. From the Apple () menu, choose System Preferences.
3. Choose Displays from the View menu to open the preferences pane.
4. Select any resolution and refresh rate that your display supports.
5. Restart your computer.

[...]

If you tried all of these steps for your display and the video issues persist, contact Apple technical support or take your Apple computer to the nearest Apple Store or Apple Authorized Service Provider (AASP) for diagnosis. If you plan to visit an Apple Retail Store, make a reservation at the Genius Bar using http://www.apple.com/retail/geniusbar/ (available in some countries only).

Note: Diagnostic fees may apply for issues not covered under warranty or the AppleCare Protection Plan (APP).

Thanks for reaching out to Apple Support Communities.

Cheers.