I am trying to run my lightroom catalog across a couple of computers one with LR CC and the other older computer is LR5.7. I need to be able to use catalog from the LR5.7 on the newer computer but it won't work with the LRCC version. If I download LR CC version from my older computer will the catalog from my existing version of LR convert to a usable format?
You may use the catalog from Lightroom 5.7 to Lightroom CC, however you need to upgrade the Catalog.
Incase you are trying to Sync the same catalog, across multiple computer, then you need to have the same version of Lightroom installed on both the computers.
The CC/6 catalog is not compatible with LR 5. Also the LR 5 catalog is not compatible with LR CC/6. To use a LR 5 catalog in LR CC/6 it must first be Upgraded. LR CC/6 makes a copy of the LR 5 catalog then Converts that copy to work with LR CC/6.
So it is not really compatible either way. But there is no way to Down Grade a CC catalog to work with LR 5.