The pair of equations y=0 and y=-5 has how many soltuions?

The equation y = 0 represents  x-axis and the equation y = -5  also represent a straight line parallel to x-axis and 5 units below the line y = 0.

We know that if two lines are parallel to each other then they don't possess any common solution. So, the pair of equations y = 0 and y = -5 don't have any common solution.