Is the game really this slow?

Find something to do during the downtime... Read a book, browse the web, etc.

Most of the last several major patch releases have had improvements to turn processing times; the biggest drain is still combat resolution, which sadly is not calculated at the speed of math. Rather, the game steps through the main combat engine at an accelerated pace (32x real time or something like that). Naturally, this has very strong diminishing returns from more powerful processors. :-\

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given that I can only manage 2-3 turns per day with a PBem game the speed of turn resolution is seldom the rate limiting step it human player speed

The single player game has got significantly faster but as Fyon says the gmae plays out all computer v computer battles as if they where strategic combats and does not use a calculation to do this as many games do.

Indeed many of the problems with the game are due to the fact that the AI empires are simulated players an approach I like but which tends to cause problems as its hard to get an AI to do what a human player can do any where as easly

This is always a tough trade off in 4X Strategy games. Do you want a faced paced game or one that offers a more in-depth game. How many times have you played a game with big battles that gives you a choice between you fighting it or the PC Auto-resolve. You sit there thinking if i control the fight I'll win while only loosing a few troops, but if i aut-resolve I may loose half or more of my forces. See, that is the computer making a dice roll or two with some percentages thrown in to determine victory and causualties.

I lean towards longer turns, but more realism. Again, its a trade off.

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Erm, well, it may be a tradeoff in SE V, but that doesn't change the fact that the AI code takes way longer to run than it should. I suspect there is some corner-cutting going on under the covers there, which causes the AI turns to spin way more cycles than they should. There is no reason the relatively simplistic AI scripts just by themselves can't run at 10-100x the speed they do, there is something else going on back there.

AI scripts are not the cause for long turn times - they are executed quite quickly. It's the movement phase (green bar) and combat phases (red bar) that contribute much more significantly to the processing time.

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So why does the movement phase take so long to run for the AI players? This is why I suggested there is corner-cutting going on - the movement takes time to process for the player, but I'm really hoping most of that is due to animations and visuals, there is no reason it shouldn't be near-instant for the computer players, provided the renderer is completely switched off (which I am REALLY hoping it is) and the relevant data structures are updated intelligently and not any more than necessary. Sure, you may not get the same pretty abstractions if you do AI movement properly, but people playing the game don't care how nice your abstractions are if the computers take 5 or 10 minutes to make their turns.
Battles, OK, I can understand - if you really want to simulate real-time battles properly, run the battles at 32x speed, which I think is what we get now. At the 3 min time limit, each battle should take a maximum of about 6 seconds, which is reasonable, though still a tad long. However, it's the long movement phases which really get me.

Even without visuals, there is still a fair amount of stuff to calculate as each ship moves... Cutting corners would involve not calculating sight radii with every hex moved, and instead skipping it all and just calculating sight after the ship is done moving. Given the AI's tendency to move single ships around, there are a lot of calculations to perform.

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