Linking two patch panels

Hi,
I will soon be upgrading our servers which will require an upgrade to our cisco switches.  Currently all cat5 cables from our offices terminate in a small rack on the Datacentre wall.  The rack has a switch in which is linked to another switch in one of our server racks.

The new cisco switches we are upgrading to will not fit in the cable rack where all the cat5 terminates.  Would it be possible that, instead of installing a switch in the cable rack, I added a new patch panel and ran another length of cat5 cables from this new patch panel into another patch panel in the server rack? I would then link up this patch panel to the new switch.  Effectively bypassing the old cable rack (except for the fact that the first run of cat5 cable terminates in a patch panel in there).

Thanks