Modulating a carrier with a single tone produces a spectrum of exactly three frequencies: the carrier itself and a symmetric pair of sidebands offset by the message frequency.
The sideband frequencies are the sum and difference of carrier and message:
\[f_{\pm} = f_c \pm f_m = 1000\ \text{kHz} \pm 5\ \text{kHz},\]
giving a lower sideband at $995\ \text{kHz}$ and an upper sideband at $1005\ \text{kHz}$.
For the amplitude, expand $A_c[1 + m\cos\omega_m t]\cos\omega_c t$ with the product-to-sum identity. Each sideband carries a coefficient of $mA_c/2$. Plugging in $m = 0.5$ and $A_c = 100\ \text{V}$:
\[\frac{mA_c}{2} = \frac{0.5 \times 100}{2} = 25\ \text{V}.\]
Both sidebands therefore have equal amplitude $25\ \text{V}$, which points to option (A). \[\boxed{995,\ 1005\ \text{kHz};\ 25\ \text{V each}}\]