When my system comes out of sleep it reboots why

See if your Mac suffered a recent kernel panic. If it did, it will save the log and it can be read out later using this technique. Cut and paste the text here for readers to analyze.

Mac OS X: How to log a kernel panic

Sounds like another flaking out 2008 Mac Pro 3,1.

https://support.apple.com/kb/TS1367

Symptoms

If your Macintosh computer won't turn on, here's how to troubleshoot it. Please keep in mind that although your computer may display similar symptoms that prevent it from showing video, this article discusses what to do if the computer won't turn on, meaning that when you press the power button:

• You don't hear a startup chime.
• You don't hear any fan or drive noise.
• The power button or power indicator doesn't light up at all.

• You may hear a startup chime.
• You may hear fan or drive noise.
• You may see the power button or power indicator light up.

Resolution

If your computer won't turn on, try each of these steps:

1. Make sure that the power cord is plugged into a working wall outlet, and that it's properly connected to the power adapter. (To check if the wall socket is working, plug in a lamp or other electrical device.)
2. Make sure that the power adapter is properly connected to the power port on the side or back of the computer.
3. Disconnect all accessories that are plugged into the computer, such as a printer, hub, or other mobile device.
4. Reset the computer's PMU, SMC, or PRAM. Refer to the instructions for your model:
   
   • Portable (iBook or PowerBook)
   • Mac mini
   • iMac
   • Power Mac
   • Mac Pro
   • MacBook or MacBook Pro
   • Other Mac computers

reset SMC For "Mac wont' turn on or boot" and related

https://support.apple.com/kb/TS1367

General purpose Mac troubleshooting guide: Isolating issues in Mac OS X

Creating a temporary user to isolate user-specific problems: Isolating an issue by using another user account

Identifying resource hogs and other tips: Using Activity Monitor to read System Memory and determine how much RAM is being used

Starting the computer in "safe mode": Mac OS X: What is Safe Boot, Safe Mode?

To identify potential hardware problems: Apple Hardware Test

General Mac maintenance: Tips to keep your Mac in top form