1. The problem asks to analyze the graph transformations for sine functions. 2. Part (a) asks the transformation mapping from $y=\sin x$ to $y=\sin 5x$. 3. Multiplying the input $x$ by 5 compresses the graph horizontally by a factor of $\frac{1}{5}$, making the period $\frac{360^\circ}{5} = 72^\circ$ instead of $360^\circ$. 4. Part (b) asks the transformation mapping from $y=\sin 5x$ to $y=\sin(5x + 10^\circ)$. 5. Adding $10^\circ$ inside the sine argument shifts the graph horizontally to the left by $10^\circ$. 6. So the overall effect is a horizontal compression by $\frac{1}{5}$ followed by a left shift of $10^\circ$. Final answers: (a) Horizontal compression by $\frac{1}{5}$. (b) Horizontal shift left by $10^\circ$.