To simplify the expression \((x+1) - (-2x-5)\), we start by removing the parentheses.
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Distributing the negative sign: \[ (x + 1) - (-2x - 5) = (x + 1) + (2x + 5) \]
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Now, combine the like terms:
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Combine the terms with \(x\): \[ x + 2x = 3x \]
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Combine the constant terms: \[ 1 + 5 = 6 \]
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Putting it all together, we get: \[ 3x + 6 \]
Thus, the simplified expression is: \[ \boxed{3x + 6} \]