To simplify this expression, we can first find a common denominator for the fractions.

(-1/8 + 1/5) - (4/8 - 4/9) - 0.05

We can rewrite the fractions with a common denominator of 40:

(-5/40 + 8/40) - (20/40 - 35/40) - 0.05

Now we can combine the fractions:

(3/40) - (15/40) - 0.05

Now we can subtract the fractions:

-12/40 - 0.05

Simplifying further:

-3/10 - 0.05

To subtract the decimal, we can rewrite it as a fraction:

-3/10 - 5/100

Now we need to find a common denominator again:

-30/100 - 5/100

Combine the fractions:

-35/100

Which simplifies to:

-7/20

Therefore, the simplified expression is -7/20.