It sounds like it is trying to go to sleep but something is waking it back up.
Try running "powercfg -LASTWAKE" in the command shell after the computer as come back to life. This should tell you what device woke the computer up. You then can disable this device from waking the system up with powercfg -DEVICEDISABLEWAKE <devicename> or through the device manager.
Thanks rsnelson... Here is the result. Is it safe to disable wake on this, or can it be done in the BIOS? What would the exact command be if I did it in a command prompt?
Wake History Count - 1
Wake History 
Wake Source Count - 1
Wake Source 
Instance Path: PCI\VEN_8086&DEV_1503&SUBSYS_201B8086&REV_05\3&11583659&0&C8
Description: Intel(R) 82579V Gigabit Network Connection
From the Control Panel->Network->Intel(R) 82579V Gigabit Network Connection Properties window:
Power Management tab shows a Wake on LAN section, with these options:
Wake on Magic Packet (checked)
Wake on Magic Packet from power off state (checked)
Wake on Pattern Match (checked)
Wake on Link (not checked)
Uncheck all the options in the control panel power management tab for the network adapter and try it again.
If that doesn't work, then inspect the powercfg -LASTWAKE result to see if is the same device or not.
I've used powercfg -DEVICEDISABLEWAKE <devicename> before and it will toggle the settings seen in the power management tab for devices in the device manager. So you should be able to do it either way.
You can also use powercfg -DEVICEQUERY wake_armed to show all devices which can wake up the computer. Entries should disappear from the list as you disable them.
I disabled my LAN and wireless keyboard/mouse and use the power button to wake the computer. One slight move of the mouse would wake the thing up which is not what I wanted.
Yes, unchecking the LAN wake options on the Network connection properties Power Management tab worked! Thank you. It works as you describe -- The keyboard and mouse do not wake the pc, but the power button does, and it is almost instantly, a second or less.
Just out of curiosity, how do you make it so a keypress or mouse click would wake the system? (this is how it was with my previous Intel DP35DP and Vista 64-bit system -- moving the mouse would not wake it, but clicking the mouse button or pressing a key would.)
I would suggest you go into the device manager, find your keyboard and mouse, and check to see if you have a power management tab where you can enable the wake up settings. Sometimes you may have to also enable the parent device (such as when you have a wireless transciever).
I am having the same issue and I don't agree that turning off Wake-On-Lan is the right fix. It doesn't answer the question of what is really causing the network device to wake the system. WOL has a legitimate purpose and should not need to be turned off. Down the road I do want the machine to be able to WOL but not every five minutes for no reason.
In my case this is a new PC I built and I have a hard time believing that something on the network is sending a magic WOL packet every five minutes to this computer. I have other Windows 7 machines with WOL enabled and don't have this issue. How can this be debugged at the next level to figure out what is making the network device.
I'll probably start a new thread on this since it is marked "answered".