I can't help weighing in on this one since I teach algebra and calculus at a university. The math symbol '<' is read 'is less than' so a mathematical sentence of the form
a < b
would be read "a is less than b" and would indicate that the number 'a' is farther to the left on a standard number line than is the number 'b'. So the answer to the original question is
In the language of Mathematics, it is correct to say '-5 is less than 2'.
I hope you will forgive me, but since I'm a teacher, I can't stop there. The original post indicated a trouble with English when dealing with negative numbers. If you were able to stick to using only the precise definitions, then there would be little ambiguity.
But nobody does that (and if they did, it would be hard for listeners to follow). The careful precision of the mathematical language makes it difficult to listen to, so we translate from Mathematics into English as we speak, and in doing so we naturally use other phrasings, synonyms. And that is where confusion starts to creep in.
In the context of this question, the most common confusion arises when people substitute the phrase "smaller than" for "less than."
Is -5 smaller than 2?
Well, if by 'smaller than' you mean a number's size (also called magnitude or absolute value), then no. The number -5 has size 5 which is larger than a number with size 2. The negative sign is simply telling you where to find it in relation to the number 0. If you mean 'farther to the left on a number line,' then yes, -5 is smaller than 2.
Summary: When comparing numbers, do you want to compare their relative locations (left-right on a number line) or their relative sizes? If the former, then use "less than". If the latter, use the whichever you like, but include the term "size" or "magnitude" or "absolute value".
And thank you for letting me expound on one of my favorite topics: The intersection between the languages of Math and English.