4 Bishops is much better than 5 in a Bishop+Fortress deck. His 5th Bishop will, on most turns, be playable on nothing, netting him one extra point. But eventually something terrible will happen to him, making up for all those extra points. The most drastic scenario is of course drawing a starting hand of 5 Bishops, as you said, which costs him 12 points, but lesser versions of this will crop up quite often. Perhaps he draws Fortress and four Bishops, into a fifth Bishop: that's just as bad. Or he draws a second Fortress, trashes it, and then draws the fifth Bishop: that costs him 9 points. Basically he needs to rely on his fifth Bishop being drawn after his fourth Fortress (or anyway his fourth village, if he has other villages). That's far from guaranteed, and he will gradually fall behind despite his better best-case turn.
Actually, I think this is slightly wrong. The odds that you will get a Bish on the bottom of the deck are .5. In that case you score 13 VP. Of the 50% of the other cases, you will have a Fortress followed by a Bish (moving from bottom up) 5/9 - so .28 overall. In this case you will score just 9 VP. In like manner we can fill out the odds and the payouts and then find a weighted expectation value. For 4 Bish we have 12 VP/turn as our expectation value, for 5 Fort/5 Bish we have 10.0 (negligably higher than 10 VP per turn). The expectation value is actually slightly higher as when we wiff (e.g. we end up with Bish x3 in hand), we leave 3 Forts on the bottom to draw at 100% odds in the top of the next hand (shuffle). Basically when you hit 13 VP, you reset, when you don't you have some compensatory skewing in the next hand to make 13 VP more likely.
So all of this is just the numbers behind your stuff above. However, nothing says we can't opportunistically trash Bish with Bish the first time we hit it. In this case, our expectation before we trash Bish with Bish is slightly more than 11.5. Still bad right? Well yes and no. If the other guy can eventually 3 pile the board, you might want to take a gamble if you are behind 1 or 2 VP. Sure you most likely will fall further behind, but you have a non-zero chance of getting ahead if you go 5 Bish (and then trash Bish with Bish when you whiff).
This gets better still if we have additional villages, one of the problems is that we care, a lot, about where the last Fort is. If you had a deck of 5 Bish/5 Fort/10 Farming villages, you really only care about drawing 4 Villages (for enough +action to play Bishop) and 1 Fort. In that setup we most likely will have plenty of actions to play all the Bishops even if the bottom of the deck is Fort x4. This makes your odds of getting 13 VP go up (non-trivial calculation). Unless I'm getting the statistics wrong here, optimal play should be to go for 5 Bish with excess villages, and trash Bish -> Bish when it first shows up, preferably with a bunch of excess villages if possible. This should be your best option when you are behind (it likely won't win, but you have a possibility of scoring >12 VP which you don't if you just mirror). Particularly if you are something like 2 VP behind and the other guy can pile out Bish (buy final Bish on his final turn), Fort, and another cantrip; you should roll the dice on Bish #5 first and then trash the sucker the first time he collides with Bish #4.
If you are slightly behind against Bish X4/Fort X5, then you likely are better off going for Bish X5 than trying to quickly snatch up some Provinces.