Three popular methods of support. (1) Diagonal brace from bottom of ac to exterior wall. Suggested angle between ac and wall 60* or greater. For attaching brace to wall,attach a horizonal 2x4 to brick with lead anchor screws. (2) Chains comeing from above ac to top of ac. Use turnbuckles on end of chains for fine tuning. (3) One or two boards running vertical from ground to bottom of ac.

From my experience, a 5000 btu window unit will only cool a 12 x 12 room at best. Not sure how hot or humid it gets where you are, Have you thought about a big exhaust fan in the attic? I had one in an old house. It was a 32" +/- belt drive one, and blew a lot of air. We would turn it on, with windows closed, except for 1 or 2 down stairs, and it would pull the air thru the whole house. Open window on a shady side of house, to pull in cooler air.

Sliding windows are not casement windows. Casement windows are the crank-out type. I have the sideways sliders so I know what you're going through. There's more work to putting a unit in with these but I like the windows so it's something to live with. Most new a/c units are much quieter than before. My old unit died and I bought a new one. Much quieter, albeit less powerful. Security is an issue with any window unit. Someone determined to get in can and will. However, any available window is also an opportunity to get in as is a door. One or two good kicks on a wood-framed door and that door is open. Wooden frames are not secure. I put my a/c unit in a room in which I don't sleep, then set up fans to circulate the air. Much less noise. If it gets really hot where you're at you might consider 2 units. A/C units don't have to be expensive. You can buy them for under $75. The smaller the unit, the cheaper, but, the benefit is that they're much easier to put in and take out as they weigh less. Everyone I've talked to about the "portable" units, that use a dryer vent hose seem to agree that they're far less efficient, much more expensive (probably 4-5 times) and not generally worth it except for extreme situations. Some have an evaporator for the moisture, which essentially puts the moisture back in the air, or else you're dumping a small container of water frequently if it's humid weather. A window unit of course drains outside when installed properly. Putting an a/c unit in isn't too tough. Remove the screen. Something on the bottom to protect the window frame and it should match the width of the a/c unit. It should be weather resistant, even if just put in a plastic bag. I then close the window around it and put in a blocker for the window opening. I like using the corrugated plastic for starters, cut to fit the opening snugly. Old campaign signs work great. They also give some insulation. I try to place it in the window tracks then tape it up good with box sealing tape and/or duct tape. Then another layer of something over that. Another sign or some cardboard, again, will give insulation too. Close the inside window onto it and then I use an old rectangular chair cushion in a plastic bag stuffed in the opening above the a/c. More insulation and seals out the weather. Then it's to seal by the a/c unit itself. Bubble wrap and chunks of foam rubber wrapped in plastic bags stuff in there and stay in place. The better taping job you do, the more "secure" the window is. They won't be able to slide it open. My old one had the flaps on the side that stayed inside so it couldn't fall out or be pulled out by someone outside. The new one isn't that way - I didn't put those things on because I wanted it easier to install and seal. Mine has a remote control which is very handy since I don't really go into the room. But that's a little more expensive. For a little extra security, cut a rod of some type to brace against the window and the frame, much like the broomstick in the sliding door feature. FWIW, my old unit was an 8800 BTU unit, the new one is something like 5500-6000. I cool the bedroom it's in, hallway and large living room with it and we had 100°+ temps and over 80° dewpoints this year. So I'm pleased with the performance of the smaller unit. Another consideration is the windows. Put some insulation on there. Insulated drapes make a BIG difference. You can make some simple window coverings though for the really hot days to help by simply using quilts and/or bubble wrap. If you're allowed, hang some of those rollup shades outside to block some of the sun and heat out. We hung some of those on my old GF's apartment balcony to shade her sliding door and it worked nicely on calm days. Another option is to help the a/c unit. Get a dehumidifier and use. Once you remove the humidity it's easier to cool the air, therefore the a/c unit works less and a higher temp will be more comfortable. Most will hold a gallon or more so they don't have to be emptied as often. They're also pretty quiet in operation.

I like ideas for repurposing but this has a couple of things that prevent it working. All will go as planed for a while and aside to problem you mentioned with t-stat,coils will begin frosting and soon ice over. Don't become discouraged,you are using your head and that's good.