To determine how many solutions the equation \(7t - 5 = -3 + 7t\) has, let's simplify it step by step.
First, we start with the original equation:
\[ 7t - 5 = -3 + 7t \]
Next, we subtract \(7t\) from both sides of the equation:
\[ 7t - 5 - 7t = -3 + 7t - 7t \]
This simplifies to:
\[ -5 = -3 \]
The equation \(-5 = -3\) is false. Since we arrived at a false statement, it indicates that the original equation has no solutions.
Thus, the final conclusion is:
\[ \text{The equation has no solutions.} \]