I know Raspberry Pi can get 4.75-5.25 Volts as input but will it be OK with 5.3V?
Your Pi will be perfectly fine. The Pi itself will be fine up to just less than 6V.
The 5V +/- 5% range is really to protect attached USB devices not the Pi.
I regularly measure 5.7V on my Pi's power supply.
The supply voltage is 5V ±5%. This allows some variation and either extreme is not ideal. 5.3V is +6% (why do you think this is the input) and is unlikely to cause any damage as the Pi has over voltage protection, but is unlikely to be triggered (depending on the tolerance of other components). Potentially this may increase current and increase the risk of the poly fuse opening.