is a 5" exhaust adequate for 2 x 600 w?

Yo guys ive recently moved to a bigger house and therefore have upgraded the size of my setup. Now using a secret jardin 240x120x200 tent. With 2x600w hps and 5 inch exhaust fan. No intake fans just passive. The fan is pretty good ive had it for a few years now and sucks strong but is this fan enough for the size of the tent and the extra lighting? I have the setup on the third floor of my house and its near my thermal storage boiler so its already quite warm in the room without the lamps on. Im worried its gona get too hot in there with that exhaust. I dont really have room to be putting extra intakes in and cant source fresh air anyway as my house is too overlooked by neighbours ive gota be careful. Its a rented house too so cant drill into wall to outside for a vent. any advice is welcome...

What is the cfm rating of the fan? Seems on the small side to me, but may be fine

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5" might be fine. That's about a stanley blower exhaust, which can cool almost exactly 2x600W HPS.

Edit: I actually just measured my stanley exhaust, and it's about 5.5", so you may be cutting it a bit close.

If you can't get fresh air in, you're gonna need a portable ac. If it's warm with lights off then its gonna get hot real quick.

What about a free standing ductless A/C unit? You would lose floor space, but might do the trick. Good luck!

everything depends on the cfm, I've seen little 4" vortexs, being used that outperform bigger fans. for two 600w lamps i'd use a 4"vortex pusher and a 4" vortex puller. Course it also depends on how hot it gets. an attic for example would need much more. A basement perhaps less.
if you want to use just one fan i'd use a 6" vortex. And no I don't work for vortex, just used their fans for waay over ten years now, with ZERO issues, just blast em with shop compressed air to clean em, and they are good as new. Without compressed air, they are a dirty bitch to clean though...
Also other variables are the distance from the light and the ventilation used
being upstairs near anything called a THERMAL anything and i'd suggest MORE fans.

an ac unit is probably your best bet, but that still creates an issue with CO2 starved air, you MUST have fresh air. Also an ac unit is usually rated at, at least 5-10 amps @115v so that's gonna blow if you have a regular circuit rated @15amps. both your lamps and fan is going to be at the limit for that circuit (actually a lil over) So unless you wire to a 220v (landlord may frown on that) or run an enormous extension cable to another circuit, you are gonna have issues.
I know it's less than what you want, but i'd suggest going with a solo 600w or a solo 1000w. I think given the information you supplied, and the lack of generous ventilation, two 600w lamps are going to cook em.
and those garden dimensions are in what, inches?

Thanks for the replies guys. I dont actually know the cfm of the fan as it was bought from a friend with no information or manual. There doesnt even seem to be anything written on it. Im pretty sure the air from my house is adequate, ive grown beasts in a spare room with only an open door for air exchange. I cant really have windows open etc as it will be a give away. The tent dimensions are cms. So its 2.4metres by 1.2 metres. I assume an ac unit will kane electricity? Is it safe to have an ac unit come on at intervals inside the tent to cool the air? I might not need it yet anyway all depends on how my new setup fares during the next couple of months as we are approaching summer.

Really hard to know until you get it hooked up. It is really all about temp controls, if you can keep the temps down you can use any size fan you want. Not that may go out the window when you need to factor in smell control. Unless you are augmenting CO2,you should be pulling enough to circulate the air in the room at least once every 5 minutes, but that is generally very easy to get just via the temp controls.