What's the terminology for whether a number is positive or negative?

Is there a word for the quality of a number to be either positive or negative? Consider this question:

What's the ... (sign/positivity/negativity, but a word that could describe either) of number x?

Also, is there an all-encompassing word for the sign put in front of a number (-5 or +5)? Word that describes both a plus and a minus sign?

The word that you are looking for is the very word that you are using and that word is sign.

If you are looking for something more "academic", then you can use its Latin variant, signum.

Context can also effect what word you might choose. For instance, in physics it's common to use the word direction in place of the word "sign."

But don't take my word for it; have a look at page $229$ of "A Handbook of Mathematical Discourse".

The search is for a PHILOSOPHICAL term to denote positive / negative. I agree that "sign" lacks something - hence, consider "polarity" and "charge".