Let's get some of the basics out of the way. Is this the best iPhone yet? Certainly. The best looking? Sure - it looks pretty much like last year's iPhone 5. Same shape and design, which is why it's not called the iPhone 6. So should you upgrade to another iPhone already?
After all, from today the new Apple mobile software, iOS 7, will be downloadable. It's free and so radically different it'll make you feel you've got a whole new phone instantly. It works with iPhone 4, 4s and 5, not to mention iPads from the second generation onwards.
Well, you might upgrade if you fancy a new colour. As before, you can choose from silver and black. Black is now called space grey, a name deemed so cool by Burberry's Chief Creative Officer Christopher Bailey that he plumped for it. Bailey recently told the Independent that if he had to choose between the five colours of the other new iPhone, the 5c, he'd pick yellow, “Because it makes you smile”.
And for the 5S, there's now gold to go with space grey and silver. That may make you smile, but if it makes you reel, note that this is a subtle, understated gold, not rose-tinted or blingtastic. It's most noticeable on the edge band or the ring round the home button on the front of the phone.
That home button is the new phone's biggest cosmetic change. But don't be fooled into thinking that means there are few changes: the differences all lie within. So that new home button is hiding a fingerprint sensor, for instance.
Recent phone innovations from major manufacturers have ranged from the superbly useful to the ridiculous. Nokia's Lumia phones have touchscreens which respond even if you're wearing gloves (useful), Samsung's Galaxy S4 has a humidity sensor built in (maybe not so much). You might think a fingerprint sensor is in the ridiculous category. How hard is it to type in a password, as many email programs now insist you must? Will it work well or are you going to be poking the sensor with increasing frustration?
Apple is not the first to put a fingerprint sensor on a phone, but it makes the system so effortless, that really doesn't matter. Setting it up takes around a minute per digit - you can register up to five fingers or thumbs and they don't all have to be yours. And though it wasn't quite 100 per cent reliable, in my tests it was almost flawless unless I had wet or dirty fingers.
And once you've got used to not typing in your passcode, keeping your phone secure isn't a chore. I was sceptical of this gimmick but it quickly won me over. Plus, of course, it's deeply cool.
The scanner, and much else in the 5s, works because the phone's processor is a significant upgrade to the last version. The A7 chip is powerful and - in my tests - remarkably fast. Web pages build in an instant, apps open quickly and so on.
The big challenges for the A7 will come when games with HD graphics arrive, for instance. But for now the signs are promising and this is a high-speed phone.
The A7 chip has a helping hand in the form of the M7 coprocessor. This measures movement in the phone's accelerometer, gyroscope and compass. It's likely that this will be exploited in new fitness apps, for example. And Apple has already found uses for it in the 5s. So the M7 can tell if you're driving or walking, for instance. So if you're following a route on Apple Maps, as you get out of the car it will automatically switch from driving to walking instructions. I've only tried this when I was cycling but it worked like a dream.
Though while we're about it Apple, how come there are no cycling instructions in Maps?
The camera on the iPhone 5s is also a substantial upgrade. It has the same pixel count as before, eight megapixels, but this time those pixels are spread across a bigger sensor so they are bigger and therefore better at pulling in light. This should mean the camera performs better in low light and certainly my experience is of a powerful, effective snapper with no discernible shutter lag, unlike many rival cameraphones. Features like burst mode, which shoots up to 10 frames a second, are achieved without seeming to tax the phone. And there are snazzy effects like slow motion for the video camera where it records at 120 frames per second. Not to mention frames and effects that can be added, in a clear nod to the influence of Instagram, though these are also available to other phones capable of iOS 7.
The iPhone 5s has decent battery life, about the same as last year's model. Though this is no mean achievement given the extra things you'll be doing with it, it would have been nice to have seen battery life increase.
This is a 4G phone and unlike the iPhone 5, will be available with 4G compatibility on Vodafone and EE now, O2 shortly and 3 by the end of the year.
Apple's timetable in the last six years has been to radically redesign the iPhone every two years. So the similarly styled 3G and 3GS were followed by iPhone 4 and 4s, 5 and now 5s. The pressure is on Apple to provide an iPhone 6 next autumn that is nothing like this model.
Since the iPhone 5 was a great-looking phone, this is too, even if it's too familiar for some. And the changes under the bonnet are genuinely game-changing. The 64-bit architecture built into the chip and the 64-bit iOS software haven't been mentioned in much of the press coverage. But they reveal a muscle and future-proofing which set the iPhone 5s ahead of its rivals in power and capability.
Those rivals now have a year to try and overtake Apple again, but for now the iPhone 5s is the most advanced smartphone around.