Here's how you should approach this problem.
You know that your ball is projected upwards at an initial velocity which we'll call v_0v0.
You also know that the distance the ball covered in its 5^(th)5th second of flight is twice the distance it covered in its 6^(th)6th second of flight.
Since the ball is projected upwards, this difference between the distances makes sense because the ball is moving against gravity, which implies that it's slowing down.
To get the distance the ball travelled in its 5^(th)5th second, calculate the distance it covered after 4 seconds of flight and subtract this distance from the distance it covered after 5 seconds of flight.
SIDE NOTE I'll skip adding the units in order to keep the text clean.
d_"4 sec" = v_0 * 4 - 1/2 * 10 * 4^2 = 4v_0 - 80d4 sec=v0⋅4−12⋅10⋅42=4v0−80
d_"5 sec" = v_0 * 5 - 1/2 * 10 * 5^2 = 5v_0 - 125d5 sec=v0⋅5−12⋅10⋅52=5v0−125
The distance it covered in its 5^(th)5th second was
Deltad_(4,5) = d_"5 sec" - d_"4 sec"
Deltad(4,5) = 5v_0 - 125 - 4v_0 + 80 = v_0 - 45
Do the same to get the distance covered in its 6^(th) second
d_"6 sec" = v_0 * 6 - 1/2 * 10 * 6^2 = 6v_0 - 180
d_"5 sec" = 5v_0 - 125
Therefore,
Deltad_(5,6) = d_"6 sec" - d_"5 sec"
Deltad_(5,6) = 6v_0 - 180 - 5v_0 + 125 = v_0 - 55
Now use the fact that
Deltad_(4,5) = 2 * Deltad_(5,6)
v_0 - 45 = 2 * (v_0 - 55)
v_0 - 45 = 2v_0 - 110
v_0 = 110-45 = color(green)("65 m/s")
