2.2.1 Inference on a Binomial Proportion - standard deviation issue

[vkjet]

While explaining a Bayesian approach it says: "Before she saw the data, the Bayesian’s uncertainty expressed by her standard deviation was 0.71. After seeing the data, it was much reduced – her posterior standard deviation is just 0.13."

But, considering beta(1,1) before the data and beta(1,5) after the data, the standard deviation should be 0.289 and 0.141 respectively.