Hmm there are plenty of materials that could last, oddly enough when mankind is long dead and gone a million years from now, our Toilets and glass would still be around and some metal depending on how it was stored, we find lots of artifacts from the bronze age. What matters the most though is how air tight the building, containers or lockers were. Like while I would be extremely hesitate, dehydrated food or vacuumed backed food should be edible, well forever as long as it's some place cold and never punctured or gotten moisture in it. So if we have a freezer that kept it's seal and temp, all of the seeds and the like should be fine, 5k years however is a bit of a stretch. Though all of this happen in our near future...
What's funny is paper items if not unsealed properly with good care will likely turn to dust as soon as we open them.
So depending on factors I have these answers.
Is it a normal locker? Likely not a damn thing minus a few items.
Those items being anything sealed well in a bag or the like, maybe plastics, ceramics, maybe any self repairing tech or items. Jewelry If not stolen should be 100% fine so long as it was from a pure material or a gemstone. Plastic keycards or id's should be fine if they didn't dry rot.
Is moisture in lockers? Likely the same but even worse conditions. I would wager next to nothing would survive this.
Sealed Lockers? Interesting possibilities. The problem is as noted, when you open them any paper items will likely turn to dust, I wouldn't eat a single open food item out of it.
Sealed items in lockers? Well clothing mostly synthetics figuratively should hold up, and ironically if the lockers were full of cold mud or the equivalent they would have remarkably well preserved contents, like the so called bog mag. Who was a hunter gatherer that fell into a bog some 8k years ago with all his tools and clothing.
Honestly I'm not expecting much out of the lockers minus some simple keepsakes or maybe writing inside of them, maybe power cells or other oddities. Clothing a possibility. The storerooms and the like is where we will likely find the most useful stuff. I suspect any sort of supply rooms or armories would have been sealed and hardened if the other humans didn't just take everything when and if they left, minus like Emergency cache's that they wouldn't need.
As to what Naomi would find, hmm.. I'm not sure, medals, a keycard? Maybe she would have some sort of computer drives that held up this long or some tools for her craft. Anything important for or to her would be in the armory or a barracks I guess. Given she's not or at least has very little augmentation, I would wager most of her personal effects would have been as old fashioned as she. Opens it, sees some photos, they all fall apart soon after.. I'll take suggestions though. Otherwise I'll wait till we hit the bigger rooms or head back to mechanics.
