To solve this expression, we can follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

5×54÷2 + 45÷5×40 + 9×5×345÷4
= 270 ÷ 2 + 9×40 + 9×5×345÷4
= 135 + 9×40 + 9×5×345÷4
= 135 + 360 + 9×5×345÷4
= 135 + 360 + 9×1725/4
= 135 + 360 + 38775/4
= 135 + 360 + 9693.75
= 495 + 9693.75
= 10188.75

Therefore, 5×54÷2 + 45÷5×40 + 9×5×345÷4 = 10188.75.