Give an explicit formula for a function F satisfying the all the following limits:

1. the limit of f(x) as x approaches negative 5 negative equals negative infinity

2. the limit of f(x) as x approaches negative 5 positive equals positive infinity

3. the limit of f(x) as x approaches infinity equals 4

4. f(5) does not exist

5. the limits as x approaches 5 does not exist for some finite value

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