To say that any expression is between a lower number L and 
a higher number H is written

      L < expression < H

"five plus the quantity of (seven minus a number)"
   ↓    ↓                     ↓     ↓       ↓
   5    +                  (  7     -       N )    

The translated expression is 5+(7-N)

Since it is between 1 and 5, we write

      1 < 5+(7-N) < 5     <-- this was all you asked for.

To solve it simplify by removing the parentheses:

       1 < 5+7-N < 5
        1 < 12-N < 5

Add -12 to all three sides:

        1 < 12-N <  5
      -12  -12    -12 
      ---------------
      -11 <   -N < -7

We divide all three sides by -1 which
reverses the inequalitiy signs

        11 > N > 7

That a case of "LARGE > MEDIUM > SMALL"
which can be written "SMALL < MEDIUM < LARGE"

         7 < N < 11

Edwin