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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