To solve this, we will first simplify each absolute value expression separately.

Absolute value of (-3):
|-3| = 3

Absolute value of (6) + 2 1/4:
|(6) + 2 1/4| = |6 + 9/4| = |(24 + 9)/4| = |33/4| = 33/4

Absolute value of (-5), (3 + 2), (3):
|-5| = 5
|(3 + 2)| = |5| = 5
|(3)| = 3

Next, combine the simplified absolute values according to the order of operations.

-3 + 33/4 - 5 - 5 - 3

Now, perform the arithmetic operations.

-3 + 33/4 - 5 - 5 - 3 = -3 + 33/4 - 13 = -3 + 8.25 - 13 = 5.25 - 13 = -7.75

Therefore, the final simplified expression is -7.75.