Step 1: Concept Molarity ($M$) is defined as the number of moles of solute per liter of solution. The formula is $M = \frac{mass}{M.wt \times Volume(L)}$.
Step 2: Meaning A 0.05 M solution contains 0.05 moles of $Na_{2}CO_{3}$ in every 1 liter of the solution.
Step 3: Analysis We are given $M = 0.05$, $M.wt = 106$, and $V = 1.0$ L. Rearranging the formula to find mass: $mass = M \times M.wt \times V = 0.05 \times 106 \times 1.0$.
Step 4: Conclusion Calculation gives $mass = 5.30$ g.
Final Answer: (D)