It is dangerous to bike with 5/36 spokes broken? I've got an old bike (not a sport bike, just an old fashioned granny bike).

The chain was super loose so I have to tighten it, the tires are fine. The rear wheel, although reasonable aligned for how abandoned the bike looks has 5 over 36 spokes broken (3 on one side and 2 on the other). I am using the bike but I am a bit scared it can break down at any moment.
Is that likely or not at all?
Definitely not recommended to ride a wheel with broken spokes. Even if the wheel does not catastrophically break and result in injury, the bike could leave you stranded.

If the bike is old and has not been maintained, you should get it inspected for other safety issues, especially proper functioning of the brakes.

There are a few questions on here about inspecting a bike for safety issues. Here's one I found after a quick search: Safety check for a used bike