5. M/J 16/P21/Q2/a, \( \mathbf{d}(\mathrm{ii}) \) (a) Solve the equation \( \frac{p-1}{7-p}=5 \)

First, let's solve the equation \( \frac{p-1}{7-p}=5 \). To eliminate the fraction, we can cross-multiply, resulting in \( p - 1 = 5(7 - p) \). This simplifies to \( p - 1 = 35 - 5p \). Next, we can combine like terms: adding \( 5p \) to both sides gives us \( 6p - 1 = 35 \). Adding 1 to both sides yields \( 6p = 36 \), and finally, dividing by 6 gives \( p = 6 \). So, the solution to the equation is \( p = 6 \).