Multiply $ \dfrac{5}{a} $ by $ b $ to get $ \dfrac{ 5b }{ a } $.

Step 1: Write $ b $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{a} \cdot b & \xlongequal{\text{Step 1}} \frac{5}{a} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot b }{ a \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5b }{ a } \end{aligned} $$

Subtract $ \dfrac{a}{3} $ from $ \dfrac{5b}{a} $ to get $ \dfrac{ \color{purple}{ -a^2+15b } }{ 3a }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3 }$ and the second by $\color{blue}{ a }$.

$$ \begin{aligned} \frac{5b}{a} - \frac{a}{3} & = \frac{ 5b \cdot \color{blue}{ 3 }}{ a \cdot \color{blue}{ 3 }} - \frac{ a \cdot \color{blue}{ a }}{ 3 \cdot \color{blue}{ a }} = \\[1ex] &=\frac{ \color{purple}{ 15b } }{ 3a } - \frac{ \color{purple}{ a^2 } }{ 3a }=\frac{ \color{purple}{ -a^2+15b } }{ 3a } \end{aligned} $$