Is (-4,0) a solution to 5x-3y=7

No it's not a solution because if u plug in the coordinate x which is - 4 and the coordinate y which is 0 into the equation you will get 5 * (-4) - 3 (0) = 7. After you get this equation you solve to see if it's fits.

-30-0=7

-30=7 - 30 doesn't equal seven therefore (-4,0) is not a solution to the equation