The value of $5+[6+(3+5)÷2]÷2$ is equal to:

To find the value of the given expression, we follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction).

The given expression is:
$5+[6+(3+5)÷2]÷2$

Step 1: Solve the innermost parentheses first
First, we calculate the sum inside the round brackets, which is:
$3+5=8$
Substituting this value back into the expression, we get:
$5+[6+8÷2]÷2$

Step 2: Solve the operations inside the square brackets
Inside the square brackets $[6+8÷2]$, we perform the division before the addition:
$8÷2=4$
Now the expression inside the square brackets becomes:
$6+4=10$
Substituting this value back into the main expression, we obtain:
$5+10÷2$

Step 3: Solve the remaining operations
In the expression $5+10÷2$, division has a higher priority than addition:
$10÷2=5$
Finally, perform the addition:
$5+5=10$

Thus, the expression evaluates to 10.