The USB spec goes up to 5.25V. The extra 50mV won't fry anything.
In fact, the device probably won't even see it. If you're drawing 2A, you'd lose 50mV by a 25milliohm resistance in the cable. Given that USB cables contain hair-thicknesses of copper these days, that's not unlikely. I've seen cables with 1 ohm resistance. In fact, to get a resistance as low as
25mohm you'd need about 0.75mm^2 of copper - that's roughly the thickness of the cable that powers your desktop PC.
A lower current draw will have less voltage drop, but any way you look at it what the device sees will be in spec. And the device would cope just fine with 5.3V straight, the DC-DC converter will have a much bigger margin.
The nominal 5.3V is already out of spec, who knows what the tolerance is on it, +/- 5% perhaps, so now it could be 300mV over, then someone charges an unprotected e-cigarette from it and ...
The USB data sockets on computers and USB Hubs often can't provide more than 500 mA (0.5 A). That's why some gadgets, eg USB disc drives, sometimes have a cable with two USB plugs - to get twice the power.
The 'next' USB standard, USB 3, will allow for more power to be delivered. Meanwhile, smartphones and tablets are usually provided with mains power adaptors which can provide more than 2 Amps, but with USB 2 style sockets so that the same USB cable can be used for charging (from a mains power adaptor or car adaptor) and for data connections with computers (which are very unlikely to have USB 3 sockets yet, as the basic specification has only just been fixed). It's possible that some computers or USB hubs may be able to provide 1 Amp or more from their USB 2 sockets, if a device is plugged in that can use it.
The difference between "5.3 volts" and "5 volts" in the markings and description of the mains chargers being argued about here, is probably down to differing national regulations rather than to any actual difference in the chargers themselves. USB chargers, and the power wire in a computer's USB socket, is required to have its output "between 4.75 volts and 5.25 volts" according to the international standard; the nominal voltage is 5. But I can imagine that some countries might require that the device be marked with the maximum voltage it can produce - and if the same country's laws round all voltage limits to one decimal place, you end up with a marking of "5.3 volts" for a device that does in fact produce no more than 5.25 volts (if you can find a volt meter accurate enough to tell the difference).
If you want to have a smartphone in the car being charged up even while it's in use (for navigation or music or whatever) then make sure the car USB charge adaptor can manage 2 Amps (some can't).
If you get a branded item from the same shop as you got the handset from, or a reputable dealer of that brand, there shouldn't be any problems. Going for a cheap alternative, especially a 'fake', may well end in tears.
A few of us were on the rounding off idea, but you've come up with a possible good reason for having to do it. IDK if it's ture or not, but it certainly sounds like a reasonable possibility.
Only disagree with the last part. I've bought a few chargers off of Ebay, for
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