Calculating atomic mass of unknown element in given compound (gas) at STP A gas $\ce{X2O5}$ has the density of $\pu{5 g L-1}$ at STP. What is the atomic mass of $\ce{X}$ given $A_\mathrm{r}(\ce{O}) = 16?$

Note: The problem is my homework for school and has been translated from another language. It is probably either missing something or it contains wrong data. Just leaving it as a cautionary tale to anyone who might also have it.
I solved, or at least tried to, by expressing the given density $\rho = \pu{5 g L^-1}$ as
$$\rho = \frac{m}{V}.\tag{1}$$
Also,
$$m = Mn\tag{2}$$
$$V = V_\mathrm{m}n,\tag{3}$$
where $n$ is the amount of substance and $V_\mathrm{m} = \pu{22.4 L mol^-1}.$ So:
$$\rho = \frac{m}{V} = \frac{Mn}{V_\mathrm{m}n} = \frac{M}{V_\mathrm{m}}\tag{4}$$
$$\pu{5 g L^-1} = \frac{M}{\pu{22.4 L mol^-1}} \quad\Rightarrow\quad M = \pu{112 g mol^-1}\tag{5}$$
Then obviously by subtracting the atomic mass of oxygen:
$$M_\mathrm{r} = 5A\mathrm{r}(\ce{O}) + 2A_\mathrm{r}(\ce{X}) \quad\Rightarrow\quad A_\mathrm{r}(\ce{X}) = 16\tag{6}$$
But that is not possible, as $16$ is the atomic mass of oxygen and there is no such thing as $\ce{O2O5}$ as far as I know. What am I doing wrong? Or is the problem wrong altogether?
Assuming it is given that $\ce{X2O5}$ behaves like an ideal gas, the best approach to do this problem is manipulating $pv = nRT$ to get the equation, which fits the given data. Suppose $m$ is the mass of the gas, $M$ is the molar mass of the gas, and $\rho$ is the density of the gas. Then $n =  \frac{m}{M}$:
$$ pv = nRT = \frac{m}{M}RT \ \Rightarrow \ M =  \frac{m}{v} \ \cdot \frac{RT}{p} = \rho \frac{RT}{p} \tag1$$
Now, you can apply $\rho = \pu{5 g L-1}$ at STP to the equation $(1)$ to find $M$. Then apply $2M_\ce{X} + 16 \times 5 = M$ to find $M_\ce{X}$, which is the atomic mass of $\ce{X}$.