hhuzzel,
On the outside chance, is it possible that this is a local ordinance? Rule that out.
Save the manufacturer's instruction sheet for the GFCI that you install. When the inspector brings it up, show him, fax him, email him, whatever, the full sheet and ask for where the "five count" limit is stated.
The UL General Information for Electrical Equipment Directory (the so-called "White Book") does not state a limit, nor is it any where in the NEC.