Step-by-step Solution:

\[ \textbf{Let us solve it cleanly and count the number of solutions.} \] \[ \textbf{Given:} \] \[ (43)_x = (y3)_8 \] \[ \textbf{Step 1: Convert both numbers to base 10} \] \[ \text{Left side:}\quad (43)_x = 4x + 3 \] \[ \text{Constraint: } x > 4 \] \[ \text{Right side:}\quad (y3)_8 = 8y + 3 \] \[ \text{Constraint: } y \in \{0,1,2,3,4,5,6,7\} \] \[ \textbf{Step 2: Equate the two expressions} \] \[ 4x + 3 = 8y + 3 \] \[ 4x = 8y \quad \Rightarrow \quad x = 2y \] \[ \textbf{Step 3: Apply base constraints} \] \[ x > 4 \Rightarrow 2y > 4 \Rightarrow y > 2 \] \[ y \le 7 \] \[ \Rightarrow \quad y \in \{3,4,5,6,7\} \] \[ \text{Corresponding values of } x = 2y: \] \[ x = 6,\,8,\,10,\,12,\,14 \] \[ \text{All obtained bases are valid.} \] \[ \textbf{Step 4: Count the number of solutions} \] \[ {5} \] \[ \textbf{Correct Answer: B (5)} \]