ELI5 for this question is hard because there are a number of ways to abstract the concept of hawking radiation, but reduce the accuracy. The top answer right now says quantum tunneling, and this isn’t just a hand wavey answer but a wrong one.
One of the ways in which Stephen Hawking first suggested to simplify it is this:
When a particle collides with its antiparticle it annhilates and gives off energy.
Empty space isn’t actually empty and has virtual particles coming in and out of existence in particle-antiparticle pairs, which will quickly collide with each other and “annihilate”.
When this happens on or near the event horizon, one particle can become trapped in the black hole and the other escapes – the energy has to come from somewhere, so it must come from the black hole. This is probably the best ELI5 answer you can get for this question.
There are a few problems with this explanation though, like are virtual particles even really real? They’re used in a bunch of calculations to simplify them, but that’s an ongoing argument in physics that’s too complicated for ELI5.
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