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Use a Taylor series with a four function calculator.

0 is a decent approximation of sin near 0.

x is a better one.

x - x^3/6 is an even better one.

x - x^3/6 + x^5/120 ...

Note that x here is in radians rather than degrees so convert (degrees * pi/180) first. Repeat until you're satisfied with how many stable digits you get

https://www.youtube.com/watch?v=3d6DsjIBzJ4

Five is small enough that you can get away with sin(5 deg) = 5pi/180