recursive definition of language “number multiple of five” L={5, 10, 15, 20,....}?

Question

Can any one define me

Answer 1

Is your meaning you want a recursive definition of that set?

1) 5 is an element of L
2) if x is an element of L then x + 5 is also an element of L

Answer 2

A recursive language in mathematics, logic and computer science, is a type of formal language which is also called recursive, decidable or Turing-decidable. The class of all recursive languages is often called R, although this name is also used for the class RP

Definitions
There are two equivalent major definitions for the concept of a recursive language:

A recursive formal language is a recursive subset in the set of all possible words over the alphabet of the language.
A recursive language is a formal language for which there exists a Turing machine which will, when presented with any input string, halt and accept if the string is in the language, and halt and reject otherwise. The Turing machine always halts; it is known as a decider and is said to decide the recursive language.
All recursive languages are also recursively enumerable. All regular, context-free and context-sensitive languages are recursive.

I am working on the later part of your question and shall come up with the solution in a separate answer.

Answer 3

The function to cal itself is known as the Recursive Function...