Solution
You should go with the higher nearest voltage range. In the case of 5.9V, the range will be 50V.
The DMM has signal conditioning circuitry, for different ranges there is attenuator circuitry that defines the attenuation ratio before the signal gets measured by the ADC.
If you try to measure 5.9 V at the 5 V range you won't get a correct measurement and the DMM will return the "Out-of-Range" and/or "NaN" value that indicates an out-of-range situation.
There is a narrow boundary above the DMM's range where the DMM will still return a meaningful measurement. It is 105% of the range, above this number the DMM will return NAN and over-range warning.