The binary code for $5$ is $0101.$ The $7-$bit even hamming code is therefore $0100101.$ We

would be able to detect an error if the data string became four. This is because the minimum

distance between the correct string and the erroneous string would be only $1,$ as the binary

code for $4$ is $0100.$ Since there is only one error, then, the parity bits will be able to both

detect and fix it$.$