A new quartz (in a white with little veining), glass or white subway tile, and under cabinet lighting will do wonders! Paint the paneling, absolutely. If you and hubs are handy, DIY the backsplash and undercabinet lighting. That will eat up your entire budget, unfortunately. Do the rest as you go (hardware, new ceiling light). Congrats on baby 2!

I love your wood cabinets, so I am glad they are staying as is. When you replace your counters, I would leave off the 4” counter part of the backsplash and just do all tile on the backsplash.

in addition to the things people mentioned, get rid of the fake plants. Agree with you, no ceiling fan in the kitchen. Maybe add some can lights.

Could you add black stained wood cabinets with glass doors above the current ones and take them to the ceilings? Also consider adding a wall behind the cabinet to the right of the fridge. does that go down some steps? I think both the back entry and the kitchen would look better with seperation from the open steps. That cabinet and wall could then be a small pantry cabinet if you wanted. It would hide the large side of the fridge and i doubt you'd miss that small counter much. You could add a black over the fridge cabinet with door to match.

lovely home. is the kitchen an addition? it doesn't feel very 1920 bungalow... and that's a compliment.
instead of painting paneling, pry a piece out carefully and see if you have drywall beneath it. it happens. if not, think about replacing the paneling with drywall .
your cabinets are in that mostly timeless continuum, and pretty. congratulations on working with what you have.
I suspect you have already pulled out the fake greenery.
your ceiling fan is probably on a separate switch. delete it, and replace it with a simple ceiling fixture will suffice. if you don't light it up, no one will notice it.
I'd live with the sink til I had a whole plan on counter, sink, and backsplash.

Since you only have a $5K budget, you can't do a lot. The kitchen doesn't look like it's in that bad of condition luckily. What we recommend is removing the backsplash and painting it (not installing a new one unless you can do it yourself). Then add undercabinet lighting and remove all fake plants and valance.

I wouldn't invest in quartz here. Once you do that you're totally locking in to a less than desirable layout.

Your best improvement is removing the tile and painting or changing it out. longer term, you should look into planning to improve the overall layout.

What is the cabinet that is built into the arch way to the dining/living room? For me at least, that would have to be removed, so that you have full access, to the open arch way. I would also want the table moved so it is more centered under the light fixture. If you really cant move it to the center, then get a swag kit and swag your light over and lower it down over the center of the table. The rest of your kitchen looks very nice and well maintained. I do agree, if you get new ones, to make sure you do not get the 4 inch piece on the back wall, and then put your backsplash on the entire space. However, the counters you have, do look to be in decent condition.

I wouldn't paint the cabinets. Remove the wood valance above the sink and hang a shade in its place. Install white counters.

Save your money. Add more. Keep adding more. 5K is just enough to ruin that space by hiring a hack or locking it under stone. Don’t make either mistake.

It looks as though you have about the same amount of countertop as I do. Just to give you an idea, my level 2 granite was $2500 installed. My stainless sink (2 bowls) was another $250 or so (I brought the template to my fabricator and they cut from that then installed the sink when they did the countertops), my backsplash ran about $700 installed, my faucet was another $150 or so. I'm in SW Florida, in a MCOL area. I would replace the fan with a simple, flush ceiling fixture since you have nice recessed lighting. Hope this helps!