This is for a rental unit, so I’m trying to keep the cost low, while also sealing it away from silverfish. I have very fine steel wool on hand as well as a tube of DAP ultra clear flexible all purpose sealant.
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I would probably plan on fixing the hole by first cutting some pieces of (looks like particle board??) down to size and reducing the overall size of the gap.
Filling that thing with foam seems like a mistake in the making should you ever need to service it again and a kind of shitry diy cus I didn’t know better solution.
The hole in the back is more concerning to me. If that goes to the exterior of the structure you need to much more seriously consider sealing.
like wise those seem like water pipes? maybe gas? so condensation should be a consideration. You should put some kind of sealing insulation around them to prevent condensation build up otherwise you’ll be setting up a mold bonanza.
Honestly, with the tools and solutions you are proposing, just get a contractor if you are the owner. you prob gonna end up setting this shit up to be redone regardless, and thats maybe a 200 dollar job