I would recommend a multi cassette heat pump. Each room can have a different temp... with remote control. HEATING and COOLING. You can pay a little more and get a 4th.

Call in an HVAC person to get ideas of what you can do.

How much do you use the upstairs? 1,400 square feet is not insignificant. Some peoples' whole houses are that size. Depending on how hot it gets in the summer where you are, to say something small would work could be an incorrect assumption. HVAC contractors have experience sizing units. You want the right size so it doesn't get overworked and can maintain a temp at least 20 degrees lower than outside in hot weather. You also don't want something oversized. If you're in a humid climate you want it to run often enough so the humidity is reduced in warm months. If you don't use the upstairs much then the type of unit Paul F. is referring to are a good solution because you can leave them off when someone isn't in the room.

All of that has to be made to work where you are. So always best to get advise from a HVAC pro who understands the budget .

"I would recommend a multi cassette heat pump."

You won't get that (installed) for your budget of $5000. Minisplits are extremely expensive to get installed (and there's no good reason why).

You can get a traditional furnace within budget but you may be pushing it to get furnace and AC for that. If you need both, you might get it with a traditional split system heatpump.

If you are trying to stay within and budget and want low operating costs, then consider installing a window unit in each bedroom. The downstairs unit will keep the house cool during the day. The window units can be used at night. It is not ideal, but it is going to cost a lot less than $5000.

MrCool heat pumps are DIY installation. Costco sells them. If the OP is not capable then someone with some tools could do it... not necessarily an expensive HVAC person.

Hello Paul, woyld these connect to the vents in the bedroom? or is it a separate installation? where would this device sit? Thanks

A virtually silent compressor sits outside your home, and the flexible copper pipes pop through the walls or run up through the walls to the desired location…. that is where the wall-mounted cassette blower is placed.
All your vents and your ductwork becomes obsolete and can be removed.

@Swiya J the system that Paul recommends in every thread is like what you would find similar in a hotel room or in an apartment in Indonesia (the "cassette" on the wall which would abandon your current forced air ductwork). That system can be a solution for certain design goals and parameters. However, no one knows your location, your house design, your heat or cooling loads, your existing unit, anything at all to even venture a guess. Even stating (besides there are "vents") that it "escalates my electric bill" doesn't even guarantee that it is an electric heating unit used in a mildly seasonal climate.

@Swiya J Don't let anyone dissuade you from checking into a mini split especially with a budget of less than $5000. I just had 4 seperate mini splits systems installed in my Santa Monica home for about $60,000! The fact that a DIY kit sells on lifetime-guarantee Costco's website for under $4000 is amazing. Do your research and make sure it is right for you. Good luck!

We also have two HVAC units - one in the cellar for the first floor, and one in the attic for the second floor. Each floor is about 1100 sq ft and we have programmable thermotats on each floor. The attic unit is above the master bedroom; we have pulldown stairs in our master closet and the unit sits just to the right at the top of the stairs for service access and before you ask, it is not noisy! When we replaced it years ago the debate was to hang it from the rafters or on the attic floor and the installers went with a soundproof platform on the floor. (The previous unit was right above our bed and it was terrible!). We live in western Massachusetts and heat pumps are just not an ideal choice; we had one previously in a condo and our electric bills were outrageous.

"The current efficiency of the MINI-SPLITS, you can reduce your heating and cooling bills by as much as 30%! How? By transferring heat – rather than generating it –mini-splits are highly efficient for heating and cooling. Plus, they avoid energy losses associated with traditional ducted systems. mini splits tend to be less expensive to operate because they don't lose as much energy through ductwork."

"Mini splits provide both heating and cooling in one to keep your home comfortable all year round. This makes them a great option for Massachusetts homes that need plenty of warmth in the winter and reliable cooling during the summer."