We'll have to have a look through the past sales of notes for a £3 and £5 dated 1 July 1833 and see. There have been a few of these notes turning up in sales. I have a scan of another £5 notes, must haul it out and see what date it is...
EDIT: Found it!
Here is a £5 note dated 1st July 1833. A definite pattern in emerging here, but only in the dates used. this £5 note is the same design as the one above, with the later date of 1st Sept 1833.
Gibbons & Williams 5 Pounds 1 July 1833