What you're seeing isn't an E and isn't a mint mark. It's an "F" which is the initial of the coin's designer James Earle Fraser. The mint mark, if there is one, would be on the back under the Words FIVE CENTS. (FWIW, the US has never used an E mint mark)
Please see the question "What is the value of a 1937 US nickel?" for more information.
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