Perhaps I am more anal than I know - but making a 5 gallon batch with 6 gallons worth of ingredients is mind boggling. You have a few options if you want your brew to finish as advertised.
Buy a bigger carboy
or
Buy 1 gallon of water + 1 stopper + 1 airlock and use water for brew and pour the excess wort in the jug and ferment separately.
or
make 6 gallons pour into your carboy and flush the leftover gallon down the drain.
or
Get a food scale from Wal-Mart if you don't have one. Weigh everything out and make the batch per the recipe by multiplying by 5 and diving by 6. Keep the excess for next batch or toss it.
The last thing I would do is mix 6 gallons of ingredients into only 5 gallons of water.
You have options - Suit yourself.