To solve this expression, we need to find a common denominator for the fractions involved. The common denominator for 28, 60, and 5 is 420.

Rewriting the expression with the common denominator:
(21/28)(420/420) - (18/60)(420/420) + (3/5)(420/420)

Simplifying the fractions:
(21/28)(420/420) - (18/60)(420/420) + (3/5)(420/420)
= (21 * 420) / (28 * 420) - (18 * 420) / (60 * 420) + (3 * 420) / (5 * 420)
= 8820 / 11760 - 7560 / 25200 + 1260 / 2100

Now, we can simplify the expression further:
= 8820 / 11760 - 7560 / 25200 + 1260 / 2100
= 3/4 - 3/4 + 3/5

Since the numerators of the fractions are the same, we can combine them:
= (3 - 3 + 3) / 5
= 3/5

Therefore, 21/28 - 18/60 + 3/5 simplifies to 3/5.