Idon't get adding integers with different
5+(-2)=?

Think of it as subtracting your adding a negative number to a positive, if the positive number is larger when adding, then your answer should end up positive if the negative number is larger your answer should be negative, in this case you could think of this problem as 5-2 instead of adding the 5 to the negative 2. so in this case your answer would be 3. if you don't get it try using a number line, those are very helpful when starting off!

Well,

5 + (-2)

"Five plus the quantity negative two."

Adding a negative quantity is the same as subtracting the positive quantity.

For example: 0 + (-1) = 0 - 1 = -1

Another situation: 0 - (+1)

You have to realize that any number (say 5, for example) without a sign in front of it is automatically positive.

Technically, if we "show signs," we will get +0 - (+1)

We can really just omit ("hide signs") the positive signs.
0 - 1 = -1

Yet another situation: 0 - (-1)

Subtracting a negative can be re-worded as "subtracting from the negative."  It sounds like it is taking away from the negative, bringing the integer closer to zero.  Subtracting a negative is the same as adding a positive.
0 - (-1) = 0 + (+1) or 0 + 1 = 1

In your case: 5 + (-2):
5 + (-2) = 5 - 2 or 3 or +3