When taking a sample of a population, the greater the sample, the closer will be the estimated parameters to the population parameters, i.e. the calculated estimators will be closer to the theoretical values. → This is because bigger samples are more representative of the population than smaller ones.
If they take a random sample of 5% of the population instead of a random sample of 10% of the population, the sample will be smaller.
If the sample taken is smaller, then the estimation of the population proportion will be less accurate, and therefore the sample proportion won't be close to the population proportion.
The correct option is C.