We can simplify the given expression as follows:
4√125 - 2√243 - 3√20 + 5√27
= 4√(5^3) - 2√(3^5) - 3√(2^2 × 5) + 5√(3^3)
= 4 × 5√5 - 2 × 3^2√3 - 3 × 2√5 + 5 × 3√3
= 20√5 - 18√3 - 6√5 + 15√3
= (20√5 - 6√5) + (-18√3 + 15√3)
= 14√5 - 3√3
Therefore, 4√125 - 2√243 - 3√20 + 5√27 simplifies to 14√5 - 3√3.