Can somebody give a little advice on hvac

I'm having ventilation issues. What is a cheap fan for exhaust in a small grow area I have two bathroom exhaust fans but they are loud as hell and don't know if I can suck air hru a DIY carbon filter would a duct booster fan be strong enough? Guess I should explain my setup it's in a shop so this summer I will be dealing with high temps
I do have a window unit but its kinda across the room so will have to rig up a dryer duct and run It to my grow area so that should settle temps/intake basically I built walls/ doors underneath my worktable insulated with styrofoam and hung some t5(will supplement with cfl)
The t5 is 4 foot and is like 240 watts I think
So my grow area ends up being about five feet long by 4 foot tall by 2 feet deep (approx)
there's a big box fan and a small oscillating fan once I run the duct for ac my temps will be great (no higher than 80) but I'm worried about summer and when I switch to flower(more lights) and very hot summers here
Well just lookin for some help I usually grow inside the house but can't now only other question is with a window unit is it possible to have a sealed room (no exhaust) or maybe some type of passive exhaust I don't know just thinking out loud I was just figuring if I keep temps cool enough with ac running (really don't wanna run it 18/6)but if I can keep temps in a good range can u go without exhaust? Wouldn't it boost co2 levels? Help sorry for sounding like a rook

forget Co2 for now, atlest until you have a hugh HID light, Co2 wont come to its right with T5HOs (not strong enough light)

best advice I can give you for summer time (I had the same problems with my 600W HPS) is to run it at night, so the dark time for the plants is mid day when temps is highest, made my temps drop from 84F to 80-82F when light was on

and I did also run a pice of ducting to a window/intake, did also help a bit ..

what made the biggest different for me was a cool hood on the 600W that made it drop from them 84-82F to 78F but since you run T5s you don't have that option, but T5s don't produce much heat either so you should be able to keep it close to ambi temps Im sure, I can (I use T5HO in my Veg room)

maby switch them two bathroom ventilations with a nice 6" ventilation, one with speed control maybe, the 6" will make less noise, specially if it run on half speed, then its next to silent, build a insulated box for it and you wont even notice the sound

Thanks for the illustration guess I should stay away from asking questions on this board makes me look like a noob
I only use t5 for veg and here in texas I think air cooled hoods are a must but this ? Was just for my veg area.. Guess it would help if my thermometer didn't go out on me the other day and wasn't thinking of adding additional co2 basically I already know I can use a fan as in the pic was just wondering if I could get away with less exhaust since ill have ac
I guess like everything else it's trial and error for me thanks for the input tho