First we convert the numbers to base ten

  23\(_{five}\)= 2 x 51 + 3 x 50

  = 10 + 3 = 13

  101\(_{five}\) = (1 x 32) + (0 x 31) + (1 x 30)

  = 9 + 0 + 1 = 10

  So, y = 13 + 10 = 23

  To convert 23 to base 2 (as in the diagram above)

Y = 23

  = 10111\(_{five}\)

Answer is B