Step 1: Understanding the Concept:
Series continuation based on a complex rotational rule.
Step 2: Key Formula or Approach:
Track the "head" of the figure.
Step 3: Detailed Explanation:
The figure rotates by 45$^{\circ}$, 90$^{\circ}$, 135$^{\circ}$... (increasing by 45$^{\circ}$ each step). Following this sequence from the 5th figure, the 6th must match figure 4.
Step 4: Final Answer:
Figure 4 is the correct continuation.