  A wide variety of applications of microwave cavities, such as measurement and
control of superconducting qubits, magnonic resonators, and phase noise
filters, would be well served by having a highly tunable microwave resonance.
Often this tunability is desired in situ at low temperatures, where one can
take advantage of superconducting cavities. To date, such cryogenic tuning
while maintaining a high quality factor has been limited to $\sim500$ MHz. Here
we demonstrate a three-dimensional superconducting microwave cavity that shares
one wall with a pressurized volume of helium. Upon pressurization of the helium
chamber the microwave cavity is deformed, which results in in situ tuning of
its resonant frequency by more than 5 GHz, greater than 60% of the original 8
GHz resonant frequency. The quality factor of the cavity remains approximately
constant at $\approx7\times 10^{3}$ over the entire range of tuning. As a
demonstration of its usefulness, we implement a tunable cryogenic phase noise
filter, which reduces the phase noise of our source by approximately 10 dB
above 400 kHz.
