> why do you need 5 volts for a rectifier tube and 6 volts for other tubes
6.3V is SO modern.
That's about Car Radio, a big fad in the 1930s. Big enough that older tubes were changed to 6.3V.
But look at the pre-car tubes. The now-forgot '27, '35, and '57 are 2.5V. 2A3 is still around, 2.5 Volts. (And never from a battery!)
2.5V was VERY common on US line-powered radios. You want a voltage which is not-large (to reduce hum), but not-tiny (so you don't need massive wires). 2.5V became somewhat standard, but other voltages were used also.
In England, after some flailing-around with 1-cell (2V) and 3-Cell (6V), 4V (2-cell, but usually AC) became the common heater voltage. Just different, no specific reason; there was very little cross-Atlantic tube-trading until the late 1930s, and by then the advantage of settling on 6.3V were obvious to all. (English cars used 12V batteries whereas US was 6V, but you can easily stack 6V tubes to a 12V source.)
There is a line of 2V tubes (single lead cell).
There are 1.4V tubes (flashlight cell).
> why do you need 5 volts for a rectifier tube and 6 volts for other tubes
Nearly all the rectifier tubes really date to pre-6.3V days. And there is NO reason the rectifier needs to be the same as the other tubes, because a rectifier filament normally sits near B+ and can't share a circuit with signal tubes who run cathodes down near B-/ground. And rectifier can be the biggest heater in the cabinet. I think they doubled-up the standard 2.5V heater for double-output thus 5V.