Why is it that the DC transfer characteristic isn't flattening out at -5 v, so it looks like a Z-shape? I did a DC sweep from -10 V to +10 V.
It seems that you're sweeping
VAC from -10V to +10V while holding
VEE steady at 5V each. Note that since you're driving the base with a voltage source, R1 and R2 have no effect on the circuit whatsoever.
The first part of your curve (from -10V to a little over -5V) is where the Q1 is cut off completely. There's no current through RC, and no voltage drop across it, so Vc sits at +5V.
The next part (from -5V to -4V) is where Q1 is starting to conduct. As the current through RC increases, the voltage drops, until Q1 is saturated. At this point, Vc is a little bit less than Vb.
From this point on, Q1 is completely saturated, and Vc tracks Vb with a small offset that represents the forward drop of the B-C junction. This can drive Vc even beyond
VCC, as you can see.