To solve the inequality \( x - 7 < 5 \), we can isolate \( x \) by adding 7 to both sides:
\[ x < 5 + 7 \]
\[ x < 12 \]
Now we need to check each of the given values:
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\( I. , 12 \): \[ 12 < 12 \quad \text{(False)} \]
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\( II. , 5 \): \[ 5 < 12 \quad \text{(True)} \]
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\( III. , 16 \): \[ 16 < 12 \quad \text{(False)} \]
The only value that satisfies the inequality \( x < 12 \) is II. \( 5 \).
Thus, the correct answer is II only.