The function $h(t)=-5t^2+20t+25$ represents the height $($in meters$)$ above the ground at time $t($in seconds$)$ of a stone thrown upwards at $t=0$ from a cliff.

$($a$)$ Write $h(t)$ in vertex form, find the maximum height $h_{\text{m}\text{a}\text{x}}$ the stone will reach and the time $t_{\text{m}\text{a}\text{x}}$ at which this height will be reached.

$($b$)$ Find the hight of the cliff, and the time when the stone hits the ground.