The max height can be found by completing the square.

`h = -5t(t-11)`

`h = -5(t^2-11t)`

`h = -5(t^2-11t+121/4-121/4)`

`h = -5((t-11/2)^2-121/4)`

`h = -5(t-11/2)^2+605/4`

The max height will be given when `-5(t-11/2)^2 ` is minimum or in other words when it is 0.

Max h = 605/4m = 151.25m

*So the max height is 151.25m.*

**Further Reading**

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