Hiss would generally be related to the tubes themselves, and would be super present with a lower output moving magnet phono cartridge, but 5mV ought to be enough. The Integration will increase the gain of the circuit, which does raise the signal to noise ratio, regardless of the tubes themselves.
If you have intermittent hiss, it could be related to garbage getting in through the power line. See if you can correlate the hiss to the operation of an appliance or dimmer in proximity to your outlets.
-PB