$\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}$
$=\sqrt{25.5}-2\sqrt{4.5}-3\sqrt{16.5}+4\sqrt{9.5}$
$=\sqrt{25}.\sqrt{5}-2.\sqrt{4}.\sqrt{5}-3.\sqrt{16}.\sqrt{5}+4\sqrt{9}.\sqrt{5}$
$=5\sqrt{5}-2.2\sqrt{5}-3.4\sqrt{5}+4.3\sqrt{5}$
$=5\sqrt{5}-4\sqrt{5}-12\sqrt{5}+12\sqrt{5}$
$=\sqrt{5}$