Can x + 2 / x-5 be simplified to 2/-5

No. Plug in some concrete numbers for x to see that the result is not always 2/-5.

Also, use paretheses when necessary. I believe the expression you're actually asking about is (x+2)/(x-5).
No, it can't be simplified like that. Cancellation only works for multiplication.
Make x=1 (or most anything except 0).

See if you get 2/-5
In Germany, we even have a saying

>Aus Differenzen und Summen
>kürzen nur die Dummen

("Only stupid people cancel from differences and sums" + it rhymes) which is perhaps not very nice but certainly helped me remember it
by
There are only two cancellations (because there are two operations):

a-a=0

a/a=0

You do not have a thing over itself. The top and bottom are different.
No, because let's say x = 2. 2+2/2-5 = - 4/3. Let's say 3; 3+2/3-5 = - 5/2. There is no cancellation for any real number.
You can only cancel stuff out if it’s multiplying. Like you can simplify 2x/5x as 2/5, but something like (x-3)/(x+6) can’t
No! (a+b)/(a-c) does not equal b/-c

Edit: However ab/(-ac)=b/-c
No - you can’t ‘cancel’ anything from the top and bottom of a fraction unless it’s a common factor of the numerator and denominator.

Example - 11/18 doesn’t cancel to 1/8.
That’s because the digit ‘1’ isn’t a factor of either - it’s just something that appears on the top and bottom of the fraction.

So it doesn’t matter that ‘x’ *appears* on the top and bottom of the fraction. It’s not a factor, so you can’t ‘cancel’ it.

I run into this misconception all the time with my students, so you’re not alone. :)