If I was work for a company for 5yrs and they did a background on me before they hired me and now decide they want do fingerprint background check on me and they fired me for something on my record from 15yrs ago that didn't have nothing to with but was fingerprint and question but was let go so what i should do now to clear my name so this won't happen to me again and do you think i can my job back ?
These questions run together but I think you are asking -
You had a background check 5 years ago. A second background check was done recently, they found a criminal record and they fired you. Is that correct? Are you saying that the 15-year old record was not yours or was not an arrest or something else?
An employer - unless you belong to a union or have a contract - can fire you for nothing. It's called employment at will.
How do you clear your name? Well, if you didn't have a record and this is all a big mistake you would need to retain an Attorney, open the criminal record, find out what the error is and correct it.
You can also apply for expungement if it IS your criminal record in SOME States for SOME crimes.
Why were you fired? Did you lie about your background? Were you fired because of your background? My guess is, no, you can't get your job back because employers are usually pretty careful with these matters - they don't make mistakes that can cause them to be sued.