Step 1: State the definition of gold number.
Gold number is the minimum mass in milligrams of a protective colloid that just prevents coagulation of $10\ mL$ of standard gold sol when $1\ mL$ of $10\%\ NaCl$ is added. Call this number $x$ for colloid A.
Step 2: Note the scaling rule.
The amount of protective colloid needed is proportional to the volume of gold sol being protected, provided the NaCl is added in the same standard proportion.
Step 3: Compare the gold sol volumes.
Standard sol $=10\ mL$, given sol $=500\ mL$. The ratio is $\dfrac{500}{10}=50$. So we have $50$ times the standard amount of sol.
Step 4: Check the NaCl proportion.
Standard uses $1\ mL$ of $10\%\ NaCl$ per $10\ mL$ sol. Here $50\ mL$ of $10\%\ NaCl$ is added to $500\ mL$ sol, which is again $1\ mL$ per $10\ mL$. So the salt is in the same standard proportion and only the sol volume scaling matters.
Step 5: Scale the protective mass.
For $10\ mL$ we need $x\ mg$. For $50\ mL$ we would need $5x\ mg$, since $500\ mL$ contains $50$ standard portions but the definition is per $10\ mL$, giving $x\times\dfrac{500}{100}=5x$.
Step 6: Conclude.
The minimum mass of A required is $5x$, matching option (3).
\[ \boxed{5x\ \ \text{(Option 3)}} \]