You are correct! We disregard the other solution because it occurs before the kick, and is also a load of nonsense.
Drawing a graph might help. What you are looking for is how long the graph of stays above the graph of . In other words, how long it is between points A and B. To do this we will solve and take the difference of the roots.
By the Quadratic Formula or otherwise:
So the time the ball is above 5m is seconds.