Solve the linear congruences
$$ 15x_j ≡ b_j \pmod {32} $$
for $b_j = 5, 7, 9, 11, 13$.
Since $\gcd(15,32)=1$, we can use Euler's Theorem,
$$ 15^{\phi(32)} \equiv 1 \pmod {32} $$
Using $\phi(32)=16$ gives us
$$ \begin{align} 15^{16} & \equiv 1 \pmod {32} \\ \\ 15 \times (15^{15} \times b_j) & \equiv b_j \pmod {32} \end{align}$$
Noting that $15^2 \equiv 225 \equiv 1 \pmod{32}$, gives us $15^{15} \equiv (15^2)^7 \times 15 \equiv 1^7 \times 15 \equiv 15 \pmod {32}$
And so
$$ \begin{align} 15 \times (15^{15} \times b_j) & \equiv b_j \pmod {32} \\ \\ 15 \times (15 \times b_j) & \equiv b_j \pmod {32} \end{align}$$
The following table shows the values of $15 \times b_j \pmod {32}$
| b_j | 15 b_j mod 32 |
| 5 | 11 |
| 7 | 9 |
| 9 | 7 |
| 11 | 5 |
| 13 | 3 |
The solutions for $x_j$ are $11, 9, 7, 5, 3$ for $b_j = 5, 7, 9, 11, 13$, respectively.