Simplify 5-3[2(3x-4)+3]

To simplify the given expression, we need to apply the order of operations, which dictates that we perform operations inside parentheses first, then multiplication and division from left to right, and finally addition and subtraction from left to right.

Let's break down the steps to simplify the expression:

Step 1: Start by simplifying the innermost parentheses.
Inside the parentheses, we have an expression: 2(3x - 4) + 3.
To simplify it, we'll apply the distributive property: multiply 2 by each term inside the parentheses.
This gives us: 6x - 8 + 3.

Step 2: Combine like terms within the parentheses.
Combine -8 and 3 to get -5.
The expression within the parentheses simplifies to: 6x - 5.

Step 3: Replace the simplified expression back into the original equation.
Now, our original equation becomes:
5 - 3[6x - 5].

Step 4: Apply the distributive property again.
Multiply 3 by each term inside the brackets: 3 * 6x = 18x, and 3 * (-5) = -15.
The equation becomes: 5 - 18x + 15.

Step 5: Combine like terms outside the brackets.
Combine 5 and 15 to get 20.
The equation simplifies to: 20 - 18x.

So, the simplified expression is 20 - 18x.