Error Code E05 occurs in Xbox 360 and caused by an issue with the Central Processing Unit (CPU) of the Xbox 360. The CPU is over heating which may be caused by loose heat sink screws inside of the Xbox 360.
To solve this error :
If you have the necessary tools and experience disassemble the Xbox 360 console unit. Be sure to turn off and unplug all power sources before disassembling the Xbox 360
Locate the eight heat sink screws. Ensure the heat sink screws are screwed down tightly.
Reassemble the Xbox 360, plug the power cord back and check to see if the error code is gone.