To simplify the expression \( 24 \div 23 - 4 \cdot 5 \) using the Order of Operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), follow these steps:
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Division and Multiplication come before subtraction.
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First, calculate \( 24 \div 23 \):
\[ 24 \div 23 \approx 1.043478 \]
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Next, calculate \( 4 \cdot 5 \):
\[ 4 \cdot 5 = 20 \]
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Now substitute these values back into the expression:
\[ 1.043478 - 20 \]
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Finally, perform the subtraction:
\[ 1.043478 - 20 \approx -18.956522 \]
Thus, the simplified expression is approximately:
\[ \boxed{-18.956522} \]