There are two things a person may mean when he says "give me five." One is, basically, give me a few minutes, which means the person needs a few minutes for a break or a few minutes in which to accomplish a task. In other cases, however, a person may say give me five to ask another person to slap his hand in congratulations, in agreement, or even as a greeting. For both uses, the phrase "give me five" is an idiom, which means it is a commonly used expressive statement rather than a literal phrase.
Often, people use idioms to express themselves. An idiom is phrase that is used to express a particular thought but does not involve the literal translation of the words involved. When someone uses the phrase "give me five" in this sense, he does not mean for the person to whom he is speaking to give him five of something. Instead, he usually means that he needs a break or an allowance of five minutes or so to get something done. He may also mean that he wants the person to slap his hand in congratulations, as a greeting, or an indication of agreement.
One example of the way a person may use the phrase "give me five" could involve a situation in which a person is asked to perform a task when he is already engaged with something else. In such a situation, he may ask the requester to give him five. This means he needs five or so minutes to finish what he is doing before he starts the new task. This same phrase may also mean the person needs a short break, or period of respite, before he continues on.
Another example to consider when trying to understand the meaning of this phrase is one in which a person is excited about something and wants to congratulate another person. For instance, team members may slap hands in congratulations for a high score, or a friend may say give me five in congratulations for getting accepted into a good college or asking an attractive girl out on a date. Additionally, an individual might use this phrase when he greets a friend instead of shaking his hand, or when he wants to indicate his agreement with a point the friend has made. In this sense, the phrase is used to congratulate or greet others in informal situations.