Using random() in update produces same random value for all

Hi,
i am trying to update a table with some random dates but that does not seem
to work.

UPDATE table
SET last_update=now()::date-(SELECT (random() * 5)::INTEGER + 1)

The updated field is always set to the same. Is there a way to make it
random for every record?

I could run it through a function but I wonder if there is s simpler way.

Thanks for any help on this

Alex