Surprised no one answered this after three weeks. It's the first time I've seen this post.
Obviously this is an old home probably built before 1965 and it is all two wire without a ground (green wire). First problem is it was clamped to the hot water line, it should have been the cold. Using copper pipe for a ground or it needs to be grounded is no longer to code. Problem is too many old homes with repairs, CPVC or PEX pipe might be used in place of copper, therefore no ground.
The best you can do here is run new 14/3 (15amp) or 12/3 (20amp) to the breaker panel. If you can run a ground wire, you should be able to run new NMC.
Another way is eliminate the ground wires and install a GFCI (it must be labeled no ground) and change both the DW and disposal with plugs.
The 5 foot rule for a ground connection to a copper pipe is for an electrical panel grounding from the pipe structure entrance.
Interior metal water piping used to extend a GEC connection to an electrode must be electrically continuous with a metal underground water pipe electrode.
www.electricallicenserenewal.com