: negative sixteen minus eight over two + 25 ÷ 5 + 1

To solve this expression, we'll follow the order of operations (also known as PEMDAS).

Step 1: Perform any calculations inside parentheses or brackets.
There are no parentheses or brackets in this expression.

Step 2: Calculate any exponents or powers.
There are no exponents or powers in this expression.

Step 3: Perform multiplication and division from left to right.
Negative sixteen minus eight gives us -16 - 8 = -24.
25 ÷ 5 gives us 5.

Step 4: Perform addition and subtraction from left to right.
Now we have -24 over two, which gives us -12.
Finally, we add -12 + 5 + 1 = -6.

Therefore, the value of the expression is -6.