Problem 45

To solve the given expression step by step, we start with the original expression and simplify it using the properties of square roots, cube roots, and absolute values.

Given expression: $\sqrt{25}+\sqrt[3]{-27}-|\sqrt{3}-2|$

1. Calculate the square root of 25: $\sqrt{25} = 5$
2. Calculate the cube root of -27: $\sqrt[3]{-27} = -3$
3. Calculate the absolute value of $\sqrt{3}-2$: Since $\sqrt{3}$ is approximately 1.732 and is less than 2, $|\sqrt{3}-2| = 2-\sqrt{3}$

Putting it all together:
\begin{align*}
\sqrt{25}+\sqrt[3]{-27}-|\sqrt{3}-2| & = 5 + (-3) - (2-\sqrt{3}) \\
& = 5 - 3 - 2 + \sqrt{3} \\
& = \sqrt{3}
\end{align*}

Therefore, the final answer is $\boxed{\sqrt{3}}$.