Hello dijinj

OK. So let me see if I understand the question. A pack of 25 cards contains five 'suits' (signs), each 'suit' containing five different cards. We simply have to find the number of possible *arrangements *of five cards, where each card is chosen from a different 'suit'.

The answer is this:

There are $\displaystyle \displaystyle 5!$ ways of arranging the different 'suits'. There are $\displaystyle \displaystyle 5$ ways of choosing each card from within its suit. So the total number of arrangements is $\displaystyle \displaystyle 5^5\times5!$.

If you didn't really mean the number of different *arrangements*, but instead you meant the number of different *selections*, then the answer is just $\displaystyle \displaystyle 5^5$.

Grandad