Voltage Difference in Superposition Theorem
I do not see any mistake in your solution.  

So to check it I will use the nodal analysis and solve for the voltage at the node where R1, R5, and R2 are connected. 

$$\frac{V_X}{R_{2}+R_3||R_4} + \frac{V_X - 5V}{R_1} + \frac{V_X - 10V}{R_5} = 0$$  

And the solution is:

\$V_X = 5.8375V \$ 

http://www.wolframalpha.com/input/?i=X%2F(11+%2B+8%2F3)+%2B+(X+-+5)%2F5+%2B+(X+-+10)%2F7+%3D+0

Therefore the voltage across \$R_5\$ is: 

\$V_5 = 10V - 5.8375V = 4.16V \$

Which means that your answer is correct indeed.