Answer
The balloon would have a volume of $1313~m^3$
Work Step by Step
We can find an expression for the original volume:
$P_1~V_1 = nRT_1$
$V_1 = \frac{nRT_1}{P_1}$
We can find an expression for the final volume:
$P_2~V_2 = nRT_2$
$V_2 = \frac{nRT_2}{P_2}$
We can divide $V_2$ by $V_1$:
$\frac{V_2}{V_1} = \frac{\frac{nRT_2}{P_2}}{\frac{nRT_1}{P_1}}$
$V_2 = \frac{P_1~T_2~V_1}{P_2~T_1}$
$V_2 = \frac{(1.00\times 10^5~N/m^2)(260~K)(5.0~m^3)}{(0.33\times 10^3~N/m^2)(300~K)}$
$V_2 = 1313~m^3$
The balloon would have a volume of $1313~m^3$.
