To simplify the expression \(12e - 5f - 7e + 3f\), start by combining like terms.
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Combine the \(e\) terms: \[ 12e - 7e = 5e \]
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Combine the \(f\) terms: \[ -5f + 3f = -2f \]
Now, put together the simplified terms: \[ 5e - 2f \]
Thus, the simplified expression is: \[ \boxed{5e - 2f} \]