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You would simply state that the function is continuous over the ranges [-5,-3) and (-3,2]. More generally, the function is continuous everywhere except for x=-3 as you stated, which can formally be written as continuous over the ranges (-Inf,-3) and (-3,+Inf). Just remember, to be rigorous, that you need to use the notation of open set "( )" and closed set "[ ]" to be correct. Infinity is always used with the open set symbol as it can't be contained.
And yea... this stuff is probably never going to be useful to you. The sort of thinking MAY be useful in some areas but it's rare.
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