Thanks for the help.

Your formula works if rearranged to
=(today()-A1)<=3
etc as the today value will always be the highest in my application.

If I have a column with cells formatted to 'custom d mmm', then enter
just the number of the day rather than the full blown 'day/month'
entry (ie 18/10 for 18th Oct), the conditional formatting will not
pick this up!

Conditional formatting seems to respond to keyboard entry of 'day/
month', and seems to disregard the underlying cell formatting setup
with 'custom'.

Am I missing something here?