First, let's simplify the mixed numbers:

5 3/4 = 23/4
9 5/8 = 77/8

So the expression becomes:

(23/4 - 77/8) - (-0.345 - 0.03)

Now, let's find common denominators:

(46/8 - 77/8) - (-0.345 - 0.03)
(-31/8) - (-0.375)

Now, simplify further:

-31/8 + 0.375
-31/8 + 3/8
=-28/8
=-7/2
=-3.5

Therefore, the final answer is -3.5.