It is: TODAY
Even if you used roman numerals, it would still require more than 5 letters.
Today (considering you'll read this answer today).
A date or Today
To write 24 January 2014 in 5 letters without using numbers kindly write 24.1.14.
The only way that's possible is on that day, you can write "today". You missed it.
If you write April 26, 2011, this contains only 5 letters, but unfortunately also contains numbers...