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A visitor from India poses the following question: "You have five fives. 55555 now, (i) Arrange the fives to get largest possible value (ii) arrange the fives to get a value equal to 1. (iii) Arrange the fives to get a value less than 1. (iv) Arrange the fives to get a value equal to 56. remember : do not use the signs +.,x,/ . But a bar or line between two digits can be helpful"
If you read my previous blog post on matchstick puzzles, you know that I don't expect there to be just one solution to this, and that anyone who thinks there is just one solution is probably being naive. Furthermore, this puzzle requires you to "think outside the box," and the person who gave you this puzzle may have a specific way they expected you to think outside the box, and therefore may not like your solutions.
I have solutions for all four parts.
They're probably not the solutions the problem poser was looking for.
And I'm not going to tell you my solutions.
Instead, I'm going to give you some pointers in directions that may help you solve the puzzle. I'll suggest to you some of the ways I "thought outside the box," and let you try to work through the possibilities to arrive at your own solutions (which might be different from mine!)
I also am not going to tell you which "outside the box" idea I used for which part of the puzzle. I don't want to give you too much help!
Ready? Here we go...
 First, I'd like to point out that your problem certainly has a typo in it. There are commas separating each of the symbols you can't use, except that between the plus and the minus, there is no comma  there is a period instead. This is certainly a typo, since the list is inconsistently displayed otherwise. This is important, because there are solutions available which make use of a decimal marker, and the decimal marker has NOT been eliminated in the rules. (If they had intended to eliminate the decimal point, they should have written: "do not use the signs +,.,,x,/" There is no way to read their actual sentence that isn't grammatically nonsensical, so we'll make the assumption that the decimal point is allowed.)
 You have hopefully thought of using exponents, but have you thought of using exponents within exponents? Or even exponents within exponents within exponents? Something like this:

Although the forward slash (division symbol) has been eliminated from use, the horizontal fraction bar has not. In fact, the statement of the rules almost begs you to use the fraction bar.
 Speaking of bars, don't forget that a bar over a digit represents a repeating digit.
 Did you know that if you flip (not rotate) a five upside down, it's a two?
 Eliminating specific operators implies that anything not specifically eliminated is fair game. Have you ever run across the "bracket" operator? The brackets represent the operation "greatest integer of." If you see the expression [3.53], that evaluates to 3. Basically, you just drop the stuff after the decimal.
 Following along with my previous observation, the "factorial" operator has not been eliminated either, so you could do 5! if you wanted, and 5! = 5(4)(3)(2)(1) = 120.
Using just those ideas, you can come up with solutions for all four parts of this puzzle. Of course, if you take it back to the person who posed the puzzle in the first place, they may say something like, "But you're not allowed to flip the fives upsidedown," or "You can't use the greatest integer function," or "You can't use a decimal point," or have some other lame excuse why your solution isn't the "correct" one.
Ask me if I care.
Nope. I don't. Thanks for asking. If they didn't want you to do certain things, they should have specified in the rules! :)
Good luck working out the rest of the puzzle. If you figure out some solutions, I'd love to hear back from you!
Professor Puzzler