By looking at the Rev Ed PICAXE website pages there are links to the datasheets for the various PIC chips forming the basis of the PICAXE parts. See
http://www.picaxe.com/What-is-PICAXE/PICAXE-Chip-Labels/
From these datasheets the absolute max ( not recommended for continuous operation) and typical operating ranges for the supply voltages are found in the ELECTRICAL CHARACTERISTICS Section of each datasheet.
Absolute maximum voltages:
08M2 Voltage on VDD with respect to VSS, ....................................................................... -0.3V to +6.5V
20M2 Voltage on VDD with respect to VSS, PIC16F1825/9 .................................................. -0.3V to +6.5V
28X2 Voltage on VDD with respect to VSS PIC18F2X/4XK22…............................................. -0.3V to +6.5V
DC Characteristics: Supply Voltage:
This is the normal operating range for chips suitable/capable of a nominal 5 V supply
08M2 == D001 VDD Supply Voltage (VDDMIN, VDDMAX)
…………………………………….. … Min 2.3 – Max 5.5 V … FOSC <= 16 MHz
…………………………………….. … Min 2.5 – Max 5.5 V … FOSC <= 32 MHz
20M2 == D001 PIC16F1825/9 …. Min 1.8 – Max 5.5 V … FOSC <= 16 MHz:
……………………………………………….. … Min 2.5 – Max 5.5 V … FOSC 32 MHz (Note 2)
28X2 == D001 VDD Supply Voltage PIC18F2X/4XK22 Min 2.3 — Max 5.5 V
Hence 5.0 Volt is definitely safe but the chip should operate correctly with a supply up to 5.5 Volts.
With respect to the Absolute Max rratings most Microchip PIC datasheets include a statement along the lines of:
Stresses above those listed under “Absolute Maximum Ratings” may cause permanent damage to the
device. This is a stress rating only and functional operation of the device at those or any other conditions above those
indicated in the operation listings of this specification is not implied. Exposure to maximum rating conditions for
extended periods may affect device reliability.