What is she barking at? Is she just barking to bark? Then I would agree on the exercise thing. But is she barking in particular at something? People walking by, dogs walking by. Etc?
Ps, don't worry too much about codes if its only five minutes. Most of the codes I've seen are that the dog must be barking excessively for an hour straight. Not five minutes. Plus, it is nearly impossible to prove because no officer wants to go sit at a house and time their dogs barking for only one complaint. I agree you should do something, but don't stress yourself out about it, it won't fix over night and you won't get in trouble over night.
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