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Step 1: Calculate the total attenuation using the formula:
\( \text{Total Attenuation (dB)} = \text{attenuation rate (dB/km)} \times \text{length of cable (km)} = -5 \text{ dB/km} \times 20 \text{ km} = -100 \text{ dB}

Step 2: Convert the transmitted power into dBm. The transmitted power is 0.1 kW, which is 100 W. Using the formula for conversion:
\( P_{dBm} = 10 \log_{10}(P_{W}) + 30 = 10 \log_{10}(100) + 30 = 20 + 30 = 50 \text{ dBm}

Step 3: Calculate the received power in dBm:
\( P_{received ext{ (dBm)}} = P_{transmitted ext{ (dBm)}} + \text{Total Attenuation} = 50 \text{ dBm} - 100 \text{ dB} = -50 \text{ dBm}

Step 4: Convert the received power back to W using:
\( P_{W} = 10^{\frac{P_{dBm} - 30}{10}} = 10^{\frac{-50 - 30}{10}} = 10^{-8} \text{ W}

Step 5: The value of x from \( 10^{-x} \text{ W} \) is 8.
Therefore, the answer is 8.