Nevermind, I changed my mind, one A/C Infinity T8 is my recommendation if you're not going to seal the room and do a mini-split.
The general rule of thumb for exhausting a grow space is to change the air 2-6 times per minute, depending on other factors like CO2 enrichment, temp, RH, etc.
5x5x6 is 150 cubic feet, so you want 300-900 CFM from your fan. The T8 does like 800CFM, so that's right at the high end. Given your temps will likely be at the high end of the spectrum, the fan is a good thing to overbuild, especially if you get the A/C Infinity T-series because they come with a programmable controller for Temp/RH that usually runs the fan much lower than its max power.
Also, a 5x5 in flower will absolutely BOMB your place with smell unless you run a fairly large charcoal filter, so you'll want a somewhat over-speced fan to pull through that much charcoal without slowing down to the point it can't move the air.
As far as the need for CO2 in a sealed room, that's definitely a consideration if you go that route, but depending on temps it might end up being your only option. It's not thermodynamically possible for an exhaust fan setup to lower temps in a grow space below the ambient temperature of the lung room outside the space. Add in the extra heat from your lighting and it's almost guaranteed that you'll fry your plants.
Unless you can get that lung room down into the 70's and keep it there ALL THE TIME then you'll probably want to consider a sealed setup. I've found the mushroom CO2 generators make a meaningful amount of CO2 if you use enough for the volume of your space. Also going to a true living soil grow style with very very large beds full of organic matter can throw off a huge amount of CO2, especially if properly colonized with some kind of saprophytic fungi.
