To multiply 3/8 by 5 1/7, first convert 5 1/7 to an improper fraction:

5 1/7 = (7*5 + 1)/7 = 36/7

Now multiply 3/8 by 36/7:

(3/8)(36/7) = (336)/(8*7) = 108/56

Next, simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:

108/56 = 27/14

Therefore, 3/8 * 5 1/7 = 27/14