To subtract these fractions, we need to find a common denominator. The least common multiple of 6 and 28 is 84.

Converting 1 to a fraction with a denominator of 84:

1 = 84/84

Converting 5/6 to a fraction with a denominator of 84:

5/6 = (5/6) * (14/14) = 70/84

Converting 21/28 to a fraction with a denominator of 84:

21/28 = (21/28) * (3/3) = 63/84

Now we can subtract the fractions:

84/84 - 70/84 - 63/84 = (84 - 70 - 63)/84 = (84 - 133)/84 = -49/84

Therefore, 1 5/6 - 21/28 = -49/84.