Sure, let's solve the expression step-by-step.
The given expression is:
[tex]\[ 5 - (21 \div 7 + 2) \div 5 + 2 \cdot 3 - 4 \][/tex]
Step 1: First, we evaluate the division inside the parentheses: [tex]\( 21 \div 7 \)[/tex].
[tex]\[ 21 \div 7 = 3 \][/tex]
Step 2: Next, we add 2 to the result of the division:
[tex]\[ 3 + 2 = 5 \][/tex]
Step 3: Now, we divide the result by 5:
[tex]\[ 5 \div 5 = 1 \][/tex]
Step 4: Then, we evaluate the multiplication:
[tex]\[ 2 \cdot 3 = 6 \][/tex]
Step 5: Finally, we substitute these values back into the main expression:
[tex]\[ 5 - 1 + 6 - 4 \][/tex]
Step 6: Perform the remaining operations from left to right:
[tex]\[ 5 - 1 = 4 \][/tex]
[tex]\[ 4 + 6 = 10 \][/tex]
[tex]\[ 10 - 4 = 6 \][/tex]
Therefore, the final result is:
[tex]\[ 6 \][/tex]
