The value of $\frac{5}{8}-\frac{1}{16}$ is
(A) larger than $\frac{3}{4}$
(D) less than $\frac{1}{2}$
(B) larger than $\frac{3}{5}$
(E) less than $\frac{7}{16}$
(C) larger than $\frac{5}{9}$
Calculating the given difference using a common denominator, we obtain $\frac{5}{8}-\frac{1}{16}=\frac{9}{16}$.

Since $\frac{9}{16}$ is larger than each of $\frac{1}{2}=\frac{8}{16}$ and $\frac{7}{16}$, then neither (D) nor (E) is correct.

Since $\frac{9}{16}$ is less than each of $\frac{3}{4}=\frac{12}{16}$, then $(A)$ is not correct.

As a decimal, $\frac{9}{16}=0.5625$.

Since $\frac{3}{5}=0.6$ and $\frac{5}{9}=0 . \overline{5}$, then $\frac{9}{16}>\frac{5}{9}$, so (C) is the correct answer.

ANSWER: (C)