To be precise, you don't die from having your spine cut off at C5. The Celiac Plexus (Solar Plexus) is derived from TH6-12 I believe, via the splanchnic nerves. It does disturb the region and your breathing but shouldn't kill you under normal circumstances.
What I consider as possibility for killing you though would be if the adrenal cortex was hit, however the adrenal cortex is not directly innervated by the Celiac Plexus, and hitting the fibers before they synapse should not trigger a lethal corticoid release.
I feel I've been studying too much neuroanatomy recently... Two more weeks until the exam. With an immunology and clinical medicine exam in between.