Check My Hard Lemonade Recipe PLZ

Trying to brew some hard lemonade this week. Only difference between my recipe and the ones I have seen on the forum is that I want to use real lemonade instead of concentrate. Here's the recipe:

4 gallons Simply Lemonade (Simply brand because it is all natural)
5 pounds of turbinado sugar
1 pound of extra light DME
1 gallon of water
peppermint sticks
yeast nutrient
White Labs California Ale Yeast

I need some help on my process. I was thinking I would boil the gallon of water and add the sugar and DME. Cool that down, put it in a 5 gal carboy along with the lemonade, yeast nutrient, and yeast. Make sure to aerate well. Rerack onto peppermint sticks. Bottle after 3 weeks.

Any advice would be greatly appreciated, thanks!

I'm no expert, but I see SO many incorrect things I wouldn't know where to start.


Edit...sorry, I was thinking lemon wine, not lemon beer.

Never mind.

Oh yea, lemon beer is probably closer, not sure where to post other than the wine forum though. Anyone see anything wrong with this recipe? Thanks.