To simplify the expression, we can start by simplifying each individual term within the parentheses.

1 + 2/3 - 5/4 = (4/4 + 2/3 - 5/4) = (12/12 + 8/12 - 15/12) = 5/12

1 - 5/4 = (4/4 - 5/4) = -1/4

2022 - 2/3 = (2022 * 3/3 - 2/3) = (6066/3 - 2/3) = 6064/3

Now we can substitute these simplified terms back into the original expression:

(5/12) - (-1/4) + (6064/3)

To add or subtract fractions, we need a common denominator. In this case, the least common multiple of 12 and 4 is 12. So we can rewrite the expression as:

(5/12) + (3/12) + (4848/12)

Now we can add the numerators:

(5 + 3 + 4848)/12 = 4856/12

Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:

(4856/4) / (12/4) = 1214/3

Therefore, the simplified expression is 1214/3.