My laptop USB port is outputting 5.8 V. Is this in tolerance?
The USB specification says 4.4 V or 4.45 V to 5.25 V for VBus. Some non-standard USB supplies will be higher to combat the voltage drop over a long wire and high current, but it is not within normal specifications.
Are you measuring under load? That would be important. Most devices will regulate down and even 5 V ICs tend to tolerate up to 6 V, so it's not a great problem.
As it turns out, my multimeter battery was under-voltage, and this was the source of seeing the high reading on the USB power. With a fresh battery I now see 5.01 V across the 5V terminals.
On a new ATX power supply I have -12.01 V, -5.01 V, 5.01 V and 12.30 V on the nominal -12, -5, 5 and 12 volt terminals.
The low battery also affected readings across precision resistors. Check your batteries.
If it's a cheap power circuit, it might need a tiny minimum load to get within the specified voltage. Would expect to see this on dollar-store USB-chargers, not from a computer!
Put a 5k resistor on it and see what it does.