WHY THE ANSWER IS NOT 5:

Let's show that 6-0+1 does not equal 5.

If you believe 6-0+1=5 then:

6-0+1=5

⇔ 6-0=5-1

⇔ 6-0=4

⇔ 6=4

Then if you admit that 6 is not 4, you must admit that 6-0+1 is not 5.

ANOTHER PROOF:

By giving precedence to addition over substraction you will get:

6-1*0+2/2=6-(1*0+2/2)

Let's re-develop the right part and check if it's correct:

6-(1*0+2/2)=6-1*0-2/2

I believe you saw what has changed here:

6-1*0+2/2 is not 6-1*0-2/2

ABOUT SUBSTRACTION:

A substration is an addition of a negative number. Hence:

6-1*0+2/2 can be written 6+(-1*0)+2/2

So you can, as you want, substract first or add first. Whatever will do.

ANOTHER CONSIDERATION:

Using a basic calculator, which does not allow to input the whole calculation at once, is like adding some parenthesis in the calcuation at every step.

So, instead of getting the result of 6-1*0+2/2 you will get the result of (((6-1)*0)+2)/2.

Let's check the last one:

(((6-1)*0)+2)/2

=((6-1)*0)/2+2/2

=(6*0)/2-(1*0)/2+2/2 which is not quite the same as 6-1*0+2/2

THUS, THERE IS ONE AND ONLY ONE ANSWER...

...which is:

6-1*0+2/2

=6-(1*0)+(2/2)

=6-0+1

=6+1

=7