For the first equation, we have:

[ {x}^{2} - 4 = 0 ]

Adding 4 to both sides:

[ {x}^{2} = 4 ]

Taking the square root of both sides:

[ x = \pm \sqrt{4} ]

[ x = \pm 2 ]

For the second equation, we have:

[ \sqrt{625} - x^{2} = 0 ]

[ 25 - x^{2} = 0 ]

Adding (x^{2}) to both sides:

[ x^{2} = 25 ]

Taking the square root of both sides:

[ x = \pm \sqrt{25} ]

[ x = \pm 5 ]

So, the solutions for the given equations are:

[ x = \pm 2, \pm 5 ]