Can I use a case/switch statement with two variables?

Yes you can also do:

    switch (true) {

     case (var1 === true && var2 === true) :
       //do something
       break;
     case (var1 === false && var2 === false) :
       //do something
       break;

      default:

    }

This will always execute the switch, pretty much just like if/else but looks cleaner. Just continue checking your variables in the case expressions.

How about a bitwise operator? Instead of strings, you're dealing with "enums", which looks more "elegant."

// Declare slider's state "enum"
var SliderOne = {
    A: 1,
    B: 2,
    C: 4,
    D: 8,
    E: 16
};

var SliderTwo = {
    A: 32,
    B: 64,
    C: 128,
    D: 256,
    E: 512
};

// Set state
var s1 = SliderOne.A,
    s2 = SliderTwo.B;

// Switch state
switch (s1 | s2) {
    case SliderOne.A | SliderTwo.A :
    case SliderOne.A | SliderTwo.C :
        // Logic when State #1 is A, and State #2 is either A or C
        break;
    case SliderOne.B | SliderTwo.C :
        // Logic when State #1 is B, and State #2 is C
        break;
    case SliderOne.E | SliderTwo.E :
    default:
        // Logic when State #1 is E, and State #2 is E or
        // none of above match
        break;


}

I however agree with others, 25 cases in a switch-case logic is not too pretty, and if-else might, in some cases, "look" better. Anyway.

var var1 = "something";
var var2 = "something_else";
switch(var1 + "|" + var2) {
    case "something|something_else":
        ...
        break;
    case "something|...":
        break;
    case "...|...":
        break;
}

If you have 5 possibilities for each one you will get 25 cases.

First, JavaScript's switch is no faster than if/else (and sometimes much slower).

Second, the only way to use switch with multiple variables is to combine them into one primitive (string, number, etc) value:

var stateA = "foo";
var stateB = "bar";
switch (stateA + "-" + stateB) {
    case "foo-bar": ...
    ...
}

But, personally, I would rather see a set of if/else statements.

Edit: When all the values are integers, it appears that switch can out-perform if/else in Chrome. See the comments.