To solve the equation \( 3i + 5 = 3i + 7 \), we can start by isolating \( i \).
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Subtract \( 3i \) from both sides of the equation:
\[ 5 = 7 \]
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This results in the statement \( 5 = 7 \), which is false.
This means that the original equation has no solutions. It suggests that there are no values of \( i \) that would satisfy the equation, indicating it is inconsistent.
Thus, the equation \( 3i + 5 = 3i + 7 \) has no solution.