Let's solve the equation step by step:
The given equation is:
\[ 7x - 6 + 3 = 5x + 2x + 5 \]
First, simplify both sides:
On the left side: \[ 7x - 6 + 3 = 7x - 3 \]
On the right side: \[ 5x + 2x + 5 = 7x + 5 \]
Now, we have: \[ 7x - 3 = 7x + 5 \]
Next, subtract \( 7x \) from both sides: \[ -3 = 5 \]
This statement is false. Since we reached a contradiction, it indicates that there are no solutions to the equation.
Therefore, the best description of the number of solutions for the given equation is that there are no solutions.