In order to determine the face values of the 2-year and 10-year swaps, you need to use a system of two equations with two unknowns. Given that the notional amount of the 5-year swap is 100, the equations are based on neutralizing exposure to level PC and slope PC.

To neutralize exposure to level PC, the equation is: $F(2) * \left(\frac{\text{DV01(2)}}{100}\right) * \text{LevelPC(2)} + F(10) * \left(\frac{\text{DV01(10)}}{100}\right) * \text{LevelPC(10)} + 100 * \left(\frac{\text{DV01(5)}}{100}\right) * \text{LevelPC(5)} = 0$

With the available data, this equation becomes: $F(2) * 0.0014421 + F(10) * 0.00396933 + 100 * 0.00296112 = 0$

Solving for $F(2)$: $F(2) = \frac{-0.296112 - F(10) * 0.00396933}{0.0014421}$

To neutralize exposure to slope PC, the equation is: $F(2) * \left(\frac{\text{DV01(2)}}{100}\right) * \text{SlopePC(2)} + F(10) * \left(\frac{\text{DV01(10)}}{100}\right) * \text{SlopePC(10)} + 100 * \left(\frac{\text{DV01(5)}}{100}\right) * \text{SlopePC(5)} = 0$

With the given data, this equation becomes: $F(2) * -0.00083505 + F(10) * 0.00001462 + 100 * -0.00063488 = 0$

Substituting the previously solved value for $F(2)$ into the second equation: $-0.579051383 * \left(-0.296112 - F(10) * 0.00396933\right) + F(10) * 0.00001462 - 0.063488 = 0$

Solving for $F(10)$: $F(10) = -46.68092564$ which corresponds to a face value of EUR 46.68 million.

Substituting this value of $F(10)$ back into the equation for $F(2)$: $F(2) = \frac{-0.296112 - (-46.68093 * 0.00396933)}{0.0014421}$

Hence, the correct answer to the question is C.