Despite its age, 1963 $5 US Notes aren't considered rare. As of 10/2010 auction prices are in the range of face value to $7 for a bill in circulated condition. A nice uncirculated one can bring $15 to $18, though.
The bill's red ink indicates that it's a United States Note, a form of currency that was issued from 1862 to 1966. They served the same purpose as Federal Reserve Notes, so the Treasury opted to consolidate all paper money under the Federal Reserve as a cost-saving move.
The 1963 $5 United States Note (red seal) is worth $18-$20 in mint uncirculated condition and $5-$8 in fine quality. A normal, wrinkled, used note is worth exactly $5 in any store.
Despite the bill's age and (by modern standards) unusual ink color, circulated ones aren't considered scarce. They might retail for $7-8 in average condition.
If your bill is crisp and uncirculated it might retail for $15-18.
Why red printing?
The use of red ink indicates the bill is a United States Note, a type of currency issued up till 1966. US Notes were essentially identical to Federal Reserve Notes in terms of design, printing, distribution, and financial backing from the Treasury. Rather than continue to print two separate types of bills the Treasury decided that it would be more cost-effective to suspend printing of US Notes, and all bills are now green-seal Federal Reserve Notes.
Serial numbers
It's normally not necessary to provide a bill's serial number. Serial numbers are counters and a security feature but rarely affect a bill's value. Some collectors will pay extra for numbers with a special pattern, e.g. 12345678, or low numbers such as 00000015.
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The value of a 1963 red seal two dollar bill is $1.00 to $1.25 more than face value if circulated. It is worth about $10.00 if uncirculated.
Please post a new, separate question with the bill's denomination.More information may be available at the following questions:"What is the value of a 1963 US 1 dollar bill?""What is the value of a 1963 US 5 dollar bill with a green seal?""What is the value of a 1963 US 10 dollar bill?""What is the value of a 1963 US 20 dollar bill?"
Red seals were standard on United States Notes for all denominations. Please check your bill's denomination and see one of the following for more information: "What is the value of a 1963 US 2 dollar bill with a red seal?" "What is the value of a 1963 US 5 dollar bill with a red seal?"
The US printed both $2 and $5 bills with red seals in the 1963 series. Please see the questions "What is the value of a 1963 US 2 dollar bill?" and "What is the value of a 1963 US 5 dollar bill?" for more information.
Please check again. The last red-seal $5 bills were dated 1963 and no US bills of any denomination are dated 1964.If the date on your bill is 1963 please see the Related Question "What is the value of a 1963 US 5 dollar bill with a red seal? "