How tolerable are DLSRs to moisture and humidity?

I'm going to south east Asia during the rainy season and I'm contemplating wether or not to bring my camera. My camera is a Nikon D5500 if that matters. What would you recommend doing? (P.s. I'm not stupid enough to use it while it's raining, my main worry is the humidity/moisture will damage the cameras electronics).

It depends.

All the digital SLR cameras that cost from over $1,000 (no lens) and more are all very robust and have environmental seals to protect the camera from dust and moisture

That said, I spent around a year total in both Southeast Asia, Equatorial Africa and the Caribbean during hurricane season with cameras which did not have such environmental seals and with just some prudent care and carrying around something like a "rain sleeve", was able to protect my cameras and lenses from the tropical environment. In addition, I had a camera bag which had a rubberized interior so that when I was caught in a downpour, my equipment could be protected

If you carry a couple of rain sleeves with you, you CAN use your camera while it is raining,

Here is a link to the camera bag similar to what I took while traveling in the tropics

Your camera is not weather sealed. You will need to protect it from the rain.

My Pentax K-50 goes where ever I go - under the hot sun, in the rain, at the beach, and yes in normally safe conditions too. Non-weather sealed dSLRs should survive humid climates. My K-x and ist DS have no problems at all working full time under the hot and humid weather here in the Philippines. Just don't bring them at the beach or shoot under a drizzle.

Bag your camera before bringing it out an air-conditioned room and wait at least 30 minutes before opening the bag outdoors to acclimatize it and prevent the lens from fogging.

Some more so than others. It depends on what level of camera you're planning on buying. For entry-level to mid-level the Pentax K-50 is the only weather and dust proof camera to choose from. Above that level all of the big three, Canon, Nikon, and Pentax have various models that are weather and dust proof.

Pack it in a peli storm case, use desiccant. (I use the rechargeable stuff)
Guaranteed to remove moisture.
Those cases are pretty robust too!

That will protect your kit while it is not in use.

If I close my case promptly between kit changes, the desiccant lasts 3-5 months before it needs baking dry.