Is this graph a bipartite graph?

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This question has come up in a CS exam that I have to take, however my solution is different from the one given and I can't see why I'm incorrect. I'd love to know what someone else thinks!

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Use a characterization of bipartite graphs: A graph is bipartite iff it does not contain an odd cycle.

In your graph, there is an odd cycle: $(v_2,v_4,v_5)$. So it's not bipartite.