sin^(2) +5 sinx -3= 0

i believe we have

sin^(2)x + 5 sinx - 3= 0      we could make a substitution and use the quadratic formula, but I prefer a graphical approach

Here it is......https://www.desmos.com/calculator/fxereunfe1

This graph is periodic and solutions occur at about  32.8 ± n360 degrees ...  and at 147.2 ± n360 degrees  {where n is an integer}