Let me solve the given mathematical expression step by step. The expression is:

$10 + [5 - \{4 - 2(3 + 1/2 - 1/4) \div 5 \, 1/2\}]$

Step 1: Simplify inside the parentheses

$3 + 1/2 - 1/4 = 3 + 0.5 - 0.25 = 3.25$

Step 2: Multiply by 2

$2 \times 3.25 = 6.5$

Step 3: Simplify inside the braces

$4 - 6.5 = -2.5$

Step 4: Divide by $5 \, 1/2$ (which equals $5.5$)

$-2.5 \div 5.5 = -0.4545 \, (\text{approximately})$

Step 5: Simplify inside the brackets

$5 - (-0.4545) = 5 + 0.4545 = 5.4545$

Step 6: Add to 10

$10 + 5.4545 = 15.4545$

Final Answer:

The result is approximately 15.4545.

Would you like me to clarify or break down any part further?

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Tip: Always calculate expressions inside parentheses