Question: How do I solve this set of nonlinear equations?

Below is the command I was trying to use to solve the set of equations. It doesn't give me an error or a result, I'm not sure if I am using it wrong or if solve is just the wrong command to use. Any advice would be greatly appreciated.

solve({beta*(chi^2*(exp(delta*rho))^2*delta^2-(1-chi*exp(delta*rho))*chi*exp(delta*rho)*delta^2) = 0.4e-1, beta*(-(1/12)*chi*exp(delta*rho)*delta^4*(1-chi*exp(delta*rho))+(7/12)*chi^2*(exp(delta*rho))^2*delta^4) = 0.8e-3, beta8*(-chi^2*(exp(delta*rho))^2*delta^3+(1/3*(1-chi*exp(delta*rho)))*chi*exp(delta*rho)*delta^3) = 0.8e-2, 2*beta*(1-chi*exp(delta*rho))*chi*exp(delta*rho)*delta = -0.8e-1, alpha+beta*(1-chi*exp(delta*rho))^2 = 5.6}, {chi, rho, alpha, beta, delta});

Thanks,

Julia