that 5" is NOT gonna cut it either for enough exhaust cfm. im guessing here, and im pretty sure im correct, you are wanting to use a booster type fan instead of a high velocity (high output) fan. the booster is nothing more than a glorified table fan stuck in a small round metal sleeve. nothing more. you can skimp out on a few grow equipment needs, lighting, and cooling are not something to skimp out on if you don't want to waste your time, money, and grow something decent.
KISS is the key for new growers, and seasoned vets alike. overthinking things can lead to failure. as can utilizing the wrong type of equipment, seeds, clones, soil, environment.
I researched for 1.5 years before I bought any equipment or bought my 1st batch of seeds. 4+ years later im doing pretty good. it helped me out tremendously what I learned before buying and attempting to grow.
there is a wealth of info about growing mj on quite a few forums. ALOT is horrible advise, some is excellent. you just need to use common sense and determine what is truth and what is garbage. take your time, and don't rush into it. it can save you a lot of money and headaches in the long run.
greenhouse, I used to run a LG 8k btu portable ac in a 4x4 w/1x600, then moved to a 5x10x7 w2x600. temps were great (max was 80* under hoods). the 8k is now my emergency backup. I now upgraded to a LG 14k BTU portable and my temps dropped 2* and turned down my 18" fans blowing under the hoods. and this is on fan speed 1, I have 3 to choose from
. I can get 62* incoming air (lowest if need be), I have mine set at 65*.