`(sqrt5+2)^2 - (8sqrt5)/(2sqrt5-4)`
`= sqrt5^2 + 2sqrt5*2 + 2^2 - (8sqrt5)/(2(sqrt5-2))`
`= 5 + 4sqrt5 + 4 - (4sqrt5)/(sqrt5-2)`
`= 5 + 4sqrt5 + 4 - ((4sqrt5)(sqrt5+2))/((sqrt5-2)(sqrt5+2))`
`= 5 + 4sqrt5 + 4 - ((4sqrt5)(sqrt5+2))/(sqrt5^2-2^2)`
`= 5 + 4sqrt5 + 4 - 4sqrt5(sqrt5+2)`
`= 5 + 4sqrt5 + 4 - 20 - 8sqrt5`
`= -11 - 4sqrt5`