Answer: D

Small Hint:

Turn subtraction of a negative into addition before combining terms

Big Hint:

Pair the positive and negative terms so the arithmetic stays small

Solution:

Subtracting a negative is the same as adding the corresponding positive number, so $$\begin{aligned} &1-(-2)-3-(-4) \\ &\quad {}-5-(-6) \\ &\quad = 1+2-3+4-5+6. \end{aligned}$$ Now combine the terms: $$\begin{aligned} &(1+2+4+6)-(3+5) \\ &\quad = 13-8=5. \end{aligned}$$

Thus, D is the correct answer.