What visa options are available for a five-month stay in Bangkok starting January 15th?

you'll have to bounce unless you want to get into a longer-term visa

Apply for a multiple entry tourist visa from the Thai Embassy - US DC. You'll need to figure out which embassy. In the US there are a few Thai Embassies servicing different areas. I recently applied for mine while I was in Indonesia. Your official residency is the US and you probably have a driver's license to prove it. The website ask eligibility questions, "where are you" and "were are you from". In both those choose US. After that, you'll enter the site and start a visa application. It will ask you the same question but slightly differently (what is your nationality and what is your legal residence). It will ask for proof documentation, the options are something like electric bill, rental contract, driver's license. You can upload your driver's license as proof that you are US residence. Your passport serves as proof of nationality.

People get caught up on the eligibility questions and many people in this group have their opinions but their opinions don't matter. The Embassy's opinions matter and so far they have favored me, a few times.

You take a little risk. The visa cost is $200. If you are denied you will loose that but I have never been denied.

The visa process takes about 2 weeks. That isn't enough time in your situation. In that case you can come across to Thailand visa exempt and return to Cambodia after you've gotten your visa. Or you could just hang-out in Cambodia for the next couple of weeks.

Get a tourist visa at the Thai embassy before you return. That will give you 60 days. You can get an extension one time for 30 days, so 90 days total. Then do a land border bounce with an agency for a visa exempt 30 day stamp and get a 30 day extension. That's 5 months.