OK, let's start from the beginning:
1) Do you have any issues with your 30W dish?
2) Do you have good signal from 30W if you connect your 5W Fransat receiver to it?
3) Do you have good signal from 5W if you connect your Hispasat receiver to it?
Pictures show that the dishes seem to be Zone 2 Sky dishes, which should be large enough for both satellites if aligned correctly. I am not sure about the LNBs there - they seem to be non-Sky dish LNBs which could be a mismatch for the dish, though the likelyhood of that causing your problems is low.
Do you have a closer picture of your 5W dish from behind? There's a tree in front of it but 5W is quite high in the sky and the tree is some distance so I don't believe it would cause you problems. Though it's hard to judge.
What kind of signal did the installer have on his meter? Like CH says, the meter can matter in this case as there are a few close proximity satellites up there. There's 4W, 5W and 7W. If he was using a cheap meter which only shows STRENGTH and not quality, then he may have aligned the dish somewhere between 5W and 7W, which would give you a combination of both satellites "power".
Can you take a long-ish stick and gently push the dish up/down/left/right without undoing the bolts while getting someone to watch the signal quality on the receiver?