I think as long as you are within the annual gift exclusion limits.. $14k/yr last I recall... you are fine.
IMO if there's not a rule against it, then I suppose you can go for it. The only thing stopping you is your own feeling about doing that.
However, it doesn't really make sense, since you're giving away $5,000 in order to save $1,000 on taxes.
you're still out $4,000. Am I missing something? Unless these are charities you will be donating to anyway, you're losing $4,000/yr.