Negative expected value; risk neutral choice
There are three type of individuals : risk averse, risk neutral and risk loving. 

Individuals evaluate risky prospects such as to maximize the expected level of their utility. So, an agent is risk averse if, at any wealth level $w$, he or she dislikes every lottery $Z$ with an expected payoff of zero, $EZ = 0$, so that : $Eu(w + Z) =&lt; u(w)$


Risk neutrality : $Eu(w + Z) = u(w)$
Risk love : $Eu(w + Z) = u(w)$


Assuming that $Eu(w + Z) = EZ$ (expected value of the lottery $Z$) => Risk neutral agent.

$Eu(w+ Z) = EZ = - 5$

$Eu(w) = 0$

An risk averse agent won't take the gamble. A risk neutral agent won't take the gamble. We don't know for the risk loving agent, depends on his utility function.