why is -5^2+4x2^3=7 according to this online calculator. We come up with -168 for the answer.

The calculator will do exponents before it does negatives and multiplications.

It evaluates  -5² + 4 x 2³ like this:

First:             -(25) + 4 x 2³             (because it does the exponent before it does the negative)

Second:        -(25) + 4 x 8               (it does the other exponent)

Third:             -25 + 4 x 8                 (it does the negative)

Fourth:           -25 + 32                     (it does the multiplication

Fifth:                     7                           (it does the addition)

If you want the calculator to square -5, put parenthese around the (-5); so enter it as  (-5)^2

Similarly, if you want the 4 and the 2 multiplied together first and that answer cubed, enter that portion as

(4 x 2)^3

I don't know how you arrived at -168.