Energy possessed by the ideal gas at \(27^{\circ}\,C\) is

\(E _1=3\left(\frac{3}{2} R \times 300\right)=\frac{2700 R }{2}\)

Energy possessed by the ideal gas at \(227^{\circ} C\) is

\(E _2=2\left(\frac{3 R }{2} \times 500\right)=1500\,R\)

If \(T\) be the equilibrium temperature, of the mixture, then its energy will be \(E _{ m }=5\left(\frac{3 RT }{2}\right)\)

Since, energy remains conserved,

\(E _{ m }= E _1+ E _2\)

or \(5\left(\frac{3 R T}{2}\right)=\frac{2700 R }{2}+1500 R\) or \(T =380 K\) or \(107^{\circ}\,C\)