For some reason, the Thai running community doesn't like 5k's. You will have to make do with 10k's. Register online. Races are now so popular in Thailand that same-day registration never exists even for smaller local races.
You might also want to try these half marathons in Bangkok.
16 Dec. 2018 Thailand International Half Marathon
13 Jan. 2019 Bitec Half Marathon
If you have an 18-19 minute 5k time, you would definitely win trophies at the smaller races and might even win them. For larger races, you would be at the front and might get 10th-20th. Adjusting for heat and humidity, your mile pace can be as much as a full minute slower. It's steaming hot in Bangkok even in December.