Noise from switch mode power supply and ground loops
Your text refers to a direct connection between the PSU DC- and the chassis, but it is not shown in your diagram. Running any connection other than the earth through the chassis is very, very bad, especially if it is steel and not the more conductive aluminum. Another bad practice is to run the DC- a different route from the DC+, as this creates inductive loops which both emit and pick up interference. Worst of all is poking other wires through the loop, thus creating a little air-cored transformer.
You need to separate out the various DC- lines and the earth; run each separately. Run the -ve line next to the +ve line wherever possible. Use a star layout wherever possible, typically bringing everything back to the main distribution block. PCB and PSU earths should be wired back to a common &quot;star earth&quot; point.
They will need to connect together at least once, at some point, and you should check whether that is already done inside the PSU and/or on any of the circuit boards. If the 0 V lines are taken to earth in lots of places, you will have to take special care over the wiring runs.
The ripple on that +5 V line is probably originating from the VME system. 10 MHz is high for a switched-mode PSU of that era, but typical of the CPU clock rates you'd find inside the VME box. Fixing up the returns and grounding might well fix that, or you just might need to filter the line inside or close to the VME box, if that has not been done already.
Hope this gives some pointers, it's just standard wiring practice.