What is the value of a 1934 US 5 dollar Federal Reserve Note?

There were about a dozen varieties of $5 note bearing that date, even though many were printed long after 1934. (Notes carry a series date rather than an issue date.) A price guide is available at the link below

Serial NumbersThe serial number of a note does not normally mean anything to its value unless it is somehow unusual; e.g. a low number like 00000001 or a pattern such as 12345678. "In God We Trust"That phrase wasn't put on $5 bills until 1963 so the fact that your bill doesn't have it is not a mistake.