A quick Google suggests that the 5D doesn't have an in-camera way to do this, but instead requires a post rename.

Personally, I use Exiv2 to read the date+time from my EXIF metadata and prefix this to the filename, precisely to avoid any possibility of overlapping numbers.

Here's the command I use to do that with:

"\path\to\exiv2.exe"  -k -v -r %Y%m%d-%H%M%S_:basename: rename _DSC*

(The _DSC* there is because my images start with _DSC prefix - meaning I can safely run the command on a mixed contents directory and only rename what I should, since nothing else starts with these characters.)

Based on this Canon MakerNote page, you can extract the serial number of the camera, which allows you to differentiate between images on different bodies. There is also a page providing details of more generic metadata.

Not as ideal as being able to configure it in the camera settings (as the 1D appears to allow; and no idea why they'd not let the 5D do it too), but at least this allows you to run a single command and get all your images renamed as you want.