In reply to Chris the Tall:
Lots of good advice on here. I'd assume the plumber has already checked the waste pipe - but have known some dodgy plumbers so maybe not
It's going to be worth your while spending a day finding out exactly what the problem is - and my experience with "muddling through" is that it involves more work and gives an inferior result, to identifying the problem properly and making a permanent fix.
How long has this problem been going on? You say the shower's been in 5 years, but I'm guessing it hasn't been leaking that long?
Get a bucket of water, and pour it carefully down the drain hole. If you get drips, then the leak is in your waste pipe, or the seal around the drain hole itself. if not, then try spraying water around the edges of the shower tray - also try getting in the shower and making a visual inspection of the seal when it's loaded. could be movement of the floorboards under load that isn't obvious when the shower is empty. If that turns out to be the case, you might get away with stripping away the old seal and resealing it with some weight in the tray - If bodging is your preferred tactic
If the grout has deteriorated to the extent that it's letting water through, then it ought to be obvious. if the grout has any cracks in it at all, then it needs reapplying. once again - if muddling through is your preferred option, then duct tape and visquine will ensure that water never touches the tiling, and can be removed when not actually showering. If you're married/living with a partner, that's a sort-term fix at best, and will probably cause you great suffering.
You might have a loose tile, which will cause the grout to fail - easy enough to fix if that's the case. carefully remove it - soak it overnight and remove the tile adhesive and grout from it, then clean up the surrounding tiles and the wall behind, then slap a dab of adhesive in each corner - reseat the tile - remember to use spacers - once the adhesive has dried, then re-grout
Like any other problem - you can't fix it until you've identified it, so the first step is to find out where the water's escaping from, and then you have to stop it getting to that point. Problems with the waste pipe are fairly easily fixed, but then you have to ask yourself why there are problems - movement of the shower tray can cause joints to pop - flexible tubing might be an answer to that.....
Sorry for the length of the post - I've never had the gift of brevity
Post edited at 10:57