TL;DR: Unfortunately, Fujifilm XF 16-80mm f/4 R OIS WR has disappointing corner softness. Agreed on weight; the Fujifilm XF 18-55mm f/2.8-4 R LM OIS is optically superior, lighter, and much more cost-effective.

Jumping in here because I've been in your shoes. Lugging a massive zoom used to be my thing because I was scared of missing shots, but tbh it just made me a target for pickpockets in crowded spots like the Trevi Fountain. Last time in Italy, switching to the Fujifilm XF 18-55mm f/2.8-4 R LM OIS made a world of difference. I was so satisfied with how it handled the heat and the crowds. Feeling safer is a huge plus when you aren't carrying a giant lens that screams expensive gear. Reliability matters too, and that little lens never let me down once, even after a few bumps in narrow alleys. No complaints at all. Quick tips for Rome:

• Grab a Peak Design Cuff Camera Wrist Strap for extra security in heavy crowds.
• Carry a spare Fujifilm NP-W235 Rechargeable Li-Ion Battery since the X-T5 can be thirsty.
• Use a discreet bag that doesnt look like a camera bag. Go with the 18-55 and spend the saved cash on better food. It works well for everything you'll see there and wont break your back.

I would suggest sticking with the Fujifilm XF 18-55mm f/2.8-4 R LM OIS for Rome. Heavy gear often ruins the experience when youre doing 20k steps a day. You might want to consider these points:

• The 18-55 is much lighter for all-day carry
• f/2.8 helps in dim cathedrals
• It stays well under your budget Be careful about prioritizing reach over your actual physical comfort.

Regarding what #1 said about "I would suggest sticking with the Fujifilm XF 18-55mm f/2.8-4 R LM OIS for Rome"

• I totally agree that weight is a massive deal-breaker! Honestly, I took that 16-80 to Florence last year and by day three my wrist was absolutely killing me... never again! Since you're rocking the X-T5, you really want glass that can actually handle that 40MP sensor. You should seriously look at the Sigma 18-50mm f/2.8 DC DN Contemporary for Fujifilm X instead. It's a technical marvel!
• Constant f/2.8 aperture is amazing for those dim Italian churches
• It's only 290g which is way lighter than both Fuji options
• The center sharpness is fantastic even wide open I switched to this lens for my last trip and the size-to-performance ratio is just unbeatable. It fits your 800 dollar budget perfectly too, leaving you plenty of cash for extra gelato!

ngl it drives me crazy how much we have to overthink this stuff just to walk around a city. its honestly ridiculous that even after dropping a couple grand on a body like the xt5 we are still stuck debating between gear that either feels like a brick or dont quite tick every box.

• fujifilm prices for mid range glass are getting out of control lately
• third party stuff from sigma or tamron always seems to have one weird catch like missing aperture rings
• brands keep chasing megapixels while our wrists actually suffer the consequences i went through the exact same spiral before my last big trip and honestly just felt like giving up by the time i had to pack. its such a headache when you just want to take some photos without feeling like a pack mule or worrying about whether the Fujifilm XF 18-55mm f/2.8-4 R LM OIS or that Fujifilm XF 16-80mm f/4 R OIS WR is actually gonna hold up. honestly its basically a scam that there isnt one perfect middle ground yet...