a grow box question

so im thinking of building a grow box, im going to go with an airconditioner so that i dont have to vent outiside of my closet. i want to use the 48 in wide by 70 in tall by 20 inch deep storage unit from lowes inside my bedroom closet and have two chambers. I already have a 400wattter that would go in the flowering part and a 2foot 2bulb T5 for the clone/mother side. my qestion, would i some how make it so that i could vent the motherside outside into the closet and have the intake for the vegatative side as a light proof intake getting its air from the flowering side that had the air conditioner. im thinking if i have the 400w with with an air conditioner cooling the air inside the whole op it would matter to vent the air from the mother side outside the box into the closet and the a/c would cool that hot air coming back into the into the box from the now hot closet air.

would cooltubing the 400w and having the a/c just bringing in air but at the right temp be best. that way the air from the 400watter and the t5 would be expeled into the closet and the a/c would provide intake and make sure it was cool enough. would a 5000 btu ac unit be sufficent.??

thanks for any feedback on my idea.

Where are you putting the ac unit? The heat from it has to go somewhere.

generally when u put an ac window unit in, the heat stays outside...

I think you are going way too far with this idea.....in theory it would work but it is overkill if you ask me. With a 400w cool tube you can make a complete independent vent system from your actual grow box. The intake tube would connect to the cool tube reflector and then lead out to the inline fan that would be pulling the heat out and away from the bulb. With a medium size fan nailed to the wall it should stay nice and warm in there....around 75-85 degrees. You can even add a room to room fan between the wall of your flower and veg room to keep air fresh in both sides.
Take a look at this picture for an idea of what I am saying. This is a flower only room but with a little imagination you could see a veg room next to it with a room to room fan passing circulation.

P.S. Do you really think a box would support an AC unit....you would have to build support legs and drip buckets to catch condensation. Not to mention the heat those things produce....and energy they use.