To simplify the expression, we will first find a common denominator for the fractions:

(-1/8 + 1/5) = (-5/40 + 8/40) = 3/40

Now we can rewrite the expression:

3/40 - (4/8 - 4/9) - 2.05

Next, we will simplify the parentheses:

4/8 = 1/2
4/9 does not simplify further

Now our expression is:

3/40 - (1/2 - 4/9) - 2.05

Next, we will simplify the parentheses:

1/2 - 4/9 = 9/18 - 8/18 = 1/18

Now our expression is:

3/40 - 1/18 - 2.05

Finally, we will subtract the fractions:

3/40 - 1/18 = (27/720) - (40/720) = -13/720

Putting it all together, our final answer is:

-13/720 - 2.05