Honestly, before you drop that much cash, what kind of subjects are you mostly shooting? That 40MP sensor on the X-T5 is realy demanding when it comes to glass... are you the type who likes to handle your own firmware updates and basic maintenance at home - like with a USB dock or whatever - or do you prefer just sending it off to a pro service center if things seem a bit soft? Some systems are way more DIY friendly than others which is something I always look at - definately makes a difference in the long run if you want to keep things sharp without the downtime... basically it depends on how much you like to tinker with your gear vs just shooting.

ngl i am in the exact same boat as you right now. just picked up the x-t5 and realizing my old kit lens just isnt cutting it with that 40mp sensor anymore... its kinda frustrating trying to find something that actually stays sharp without spending a fortune. ive been doing a ton of research and i think the Sigma 18-50mm f/2.8 DC DN Contemporary for Fujifilm X might be the best bet for us. its super sharp and way more compact than the fuji or tamron options mentioned above. plus, its usually around $500 so it fits your budget perfectly. one thing i like from a diy standpoint is that you can handle all the firmware updates yourself right through the camera body menu, so you dont have to worry about sending it away if there are compatibility issues later. definitely worth a look if you want that constant f/2.8 without the massive size tho.

Fujifilm 16-80mm f/4. Owned it 3 years; sharp enough for me, versatile, and within budget.

Skip the hype. Tamron 17-70mm f/2.8. Sharp enough, and often found used around $500.

Tamron's getting amazing reviews! See if it beats Fuji; check independent tests, though!

Consider Tamron. Cheap insurance for great photos, and safer than missing the shot! $700.