To solve these expressions, we can follow the order of operations (PEMDAS/BODMAS):

1. Evaluate the expression inside parentheses/brackets first:
a. For the first expression, we have (5.14 - 65)^3 + 5 = (-59.86)^3 + 5.
b. For the second expression, we have 2023 - 25^2 : 5^3 + 27.
c. For the third expression, we have 2^3 x 27 - 3^2 x 9 - 81.

2. Next, perform any exponentiation (powers):
a. For the first expression, (-59.86)^3 ≈ -208,150.5.
b. For the second expression, 25^2 = 625 and 5^3 = 125.
c. For the third expression, 2^3 = 8 and 3^2 = 9.

3. Then, perform any multiplication and division from left to right:
a. For the first expression, we have -208,150.5 + 5 ≈ -208,145.5.
b. For the second expression, 625 ÷ 125 = 5.

4. Finally, perform any addition and subtraction from left to right:
a. For the first expression, 130 - (-208,145.5) ≈ 208,275.5.
b. For the second expression, 2023 - 5 = 2018.
c. For the third expression, 8 x 27 - 9 x 9 - 81 = 216 - 81 - 81 = 54 - 81 = -27.

Therefore, the simplified expressions are:
1. 750 + 208,275.5 = 208,925.5
2. 2018
3. -27