I have Lightroom cc on mu work desktop. My home laptop is running Lightroom 5. Even though I have a subscription to CC, the laptop is old and only a 32 bit system, so I cannot upgrade the software. Can I use the same master catalog on an EHD between both computers?
No, the same master catalog would not be accessible by two different versions of Lightroom.
Each version of Lightroom works on different catalog.
You will have to maintain different catalogs on both the machines.
Also, Lightroom 5 catalog can be easily upgraded to Lightroom CC however the vice versa is not possible.
LR5 and LR 6/cc use two different formats for the catalogs. Thus LR5 and LR6 cannot share them.
If you had the two computers using the same LR version, the EHD would be a great way to share the catalog and images between the two.