• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

5.3v on 6SN7 filament?

Let me guess - you are rectifying a 5V winding originally intended to supply the tube rectifier heater/cathode.

I've done this myself BUT using schottky diodes. In the amp concerned, a 5V 2A winding with schottky diode bridge and 10,000uF/25V electrolytic pushed 5.95V DC into a 12AX7 heater (0.3 Amps draw) very nicely.
I used 4 off 1N5822 (40 Volt 3 Amp) schottky diodes for the bridge.
These things aren't real cheap but when I looked at replacing 2 of them with a MBR20100CT (dual 100V 20A with common cathode in a TO-220 pack) to save some bucks I found that the voltage drop was significantly higher.
Looking at the heater supply with a CRO (in circuit with the whole amp running) I did see a few small spikes projecting out of the ripple which went away when I sat the whole supply on a +60V DC supply derived from the main HT.

Heater Voltage Specification is +/- 5%. 6.3 - 5% is 5.97V. As far as I'm concerned the 5.95 is "in spec" (ish) whereas 5.3 is not.