Which digit will appear in the 534th place after the decimal point in the decimal representation of $\frac{5}{13}$?
The decimal representation of $\frac{5}{13}$ is $0.\overline{384615}$, which repeats every 6 digits. Since 534 is a multiple of 6, the 534th digit is the same as the last digit in the repeating block, which is $\boxed{5}$.