....You need to give us the denomination and the country of origin for the coin. All you told us is that a coin minted in 1965 with Elizabeth II's face on it (and all Dei Gratia Regina FD means is basically By the Grace of God Queen and Defender of the Faith).
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You have a British crown coin dated 1965. The words "ELIZABETH II DEI GRATIA REGINA F.D." are abbreviated latin for "Elizabeth the Second, by the Grace of God, Queen [and] Defender of the Faith." The image on the back is of former Prime Minister Winston Churchill, who died in January of 1965.
The face value of the coin (which does not actually appear on the coin) is one crown. This equates to 5 shillings, or 1/4 of a pound. While the coin has been demonetized in light of Britain's move to decimalization in 1968, the face value would equate to about 41 US cents at current exchange rates (as of late October 2009).
Numismatically, the coin can usually be purchased for a US dollar or so in Uncirculated condition, and for less than that in circulated condition.