Do you realize that you don't have a spice model for Q5? I'm guessing you got that error message, and ignored it, so LTSpice uses a VERY basic model. This model has a beta of 100 at any collector current, and it has nothing to reduce switching speed; no capacitance, no storage time, no ft. Real high power bipolar transistors generally have very slow switching speeds. In effect, the generic model is a current-controlled switch. It does have a base-emitter diode, but that only serves to slightly reduce the base current.
I could not find a spice model for Q5 (FLJ9620). You could use a different transistor. In your simulation, the collector voltage is only reaching 50V, but I suspect it will go higher if you ever get it to work...
You can't damage a transistor in a simulation.
EDIT: Have you considered a MOSFET? Seems to me that would be a better choice.