My battery is stuck!

Check to see if it's swollen; the D5300 is old enough this is enough of a concern enough I would pull any battery over 5 years out of service as a precaution as it leads to this problem.
Yeah, my rule for cameras is brutal:

• New: 3 years have a new battery ready at all times/5 end of service (recycle w/ 5Y note). Ex: If I bought a full frame Sony mirrorless camera to properly use my Minolta glass and the LA-EA adapter in 2023, I would consider it "due" for a new pack in 2025 but run the old pack as a reliable backup until 2025-2026, depending on wear.
• Used camera w/ battery: Can be situational.
  • If the camera has a way to check the health like the Canon LP-E17: Based on the health and DOM of the pack (if printed, otherwise it PROBABLY came with the camera and I need to go off of the camera release year to guestimate it). If it's still excellent I generally have no qualms about running the pack*. Ex: 2015 DOM Canon LP-E17, perfect health per camera.
    *UNLESS I need to be absolutely sure of my batteries.
  • No tracking: 5 years max runtime before noting it as a spare pack, to be replaced. If it still works well I won't waste it but I won't chance it for most things.
  • Jumped: Regardless of DOM, 3-year max service, 1-year replacement; immediate if I did not do it or 2nd jump. The reason for this? The jump procedure can be brutal, especially if you jump a battery charged over 5V with a 9V battery; you probably damaged it a bit. Now if you match it (Ex: 5V jump) or undervolt it and go for a longer pre-charger jump is less harmful by throwing a 9V battery at the problem. NO EXCEPTIONS.
    • The reason for this is people who do not know the problem with this hack tend to do it multiple times and trash the battery, or make it a future hazard. It's not worth trying to squeeze a few charges out of these heavily jumped packs.

As a general rule, I carry 2 spares+1 in the camera and usually buy the batteries when I see them unless there's an immediate need or it's older and harder to find in stores. How I usually run them is I will put the oldest one in the camera (outside of heavily jumped ones, those get scrapped and I will get 3). As a general rule with battery replacement cycles, I consider ANY battery the camera came with if purchased used as "consumed", in the sense if it has issues down the line I will replace it, especially older used prosumer cameras which run circles around the "new" entry-level options, even 2-3 generation old high end. Some of them are old enough that the original pack is "well-loved" enough (poor runtime) I don't want to run it because of how often I need to swap it and avoid THIS problem. You often get a good deal on that T6i when the T8i or T7 is more expensive than what you got that T6i for.

The reason for this wide gap? For used cameras, I don't know the age of it and most people do not weigh the risk of expansion vs. the time wasted on hacks like this, it's about runtime issues. As such, it's easier to consider it "consumed" and buy new ones before it becomes a problem (but use it as long as it holds a charge safely as a non-production pack)!
NOTE: For jumped packs, these can also be a liability once it's done (even once) to a point I will do it in a jam with a max time of 10-15 minutes, otherwise the pack is "unrecoverable". This comes with the acceptance IT WILL damage the battery a bit. As such, they get the hardest "replace by" deadline; even if it's a nuisance to buy one with others. Not frying my camera because it was jumped and won't budge...

If it is, what you may be able to do (with caution!) is stick a thin tool with adhesive on it (permanent is fine, as you will scrap the battery). PULL THE CAMERA FROM SERVICE UNTIL THIS PACK IS REPLACED! DO NOT REUSE IT! Out of service>permanently attached card. Heck, I'd super glue the card or "ruin" the contacts with glue once I have the battery out of the camera as insurance.
A cut plastic card (like a spent gift card) should be enough, so avoid metal at ALL costs unless you run out of options. You also want to avoid the SD card slot area, if it's anything like the Canon DSLRs where they're both there except the i series and the RF bodies.

This is an EXCELLENT EXAMPLE of why I discard used batteries:

Both are from 2014 so likely original to the camera and one of them is either a Korean import or a high-grade knockoff meant to pass as a Canon battery. Nope nope nope, they're already from 2014 AND one is suspicious. Now yes, I may need to keep these for the return period but once that's over I can discard them without consequence. I may run the real pack-in 2014 battery until it's too old, but I will not be using that knockoff.

I also recently ran into problems with an a6000 which came with 4 batteries (3 clones/1 OEM Sony). One of the knockoffs swelled in storage outside of the camera so I was able to catch it and mark it as bad; there's a 2nd one that may be going out I no longer trust being a knockoff with similar failure signs. 50% dud rate and it's on the cloned packs. Why in the world would I trust these things when the camera itself wasn't cheap? I'll run them until they die (and note them as coming from THAT camera) but no way would I take them out unless I was using it as an emergency spare with my 50% problem rate and it's just the clones!!!