The problem with air dielectric cables is moisture can get in them. Once water gets in the efficiency of the cable will decrease due to high dielectric loss from the water and increased resistive losses from corrosion. Water's dielectric constant is also very different from air, and so will change the characteristic impedance of the cable.
You might think if the cables are properly sealed it's no problem. However sealing is much harder than it would seem. As the temperature of the cable changes due to weather so does the pressure inside it. When the temperature decreases the cable will literally suck in air.
Consider a cable that's been baking in the sun, and then a thunderstom rolls in. The temperature decreases, and the cable sucks in humid air from the storm. Water vapor can change the impedance of the cable. That vapor can also condense into water, causing bigger and irreversible problems.
Some air dielectric cables may be specified for unpressurized use in indoor environments, but I am not aware of any that recommend unpressurized use outdoors. A couple excerpts from the Heliax installation manual make the point that your HJ5-50 should be pressurized:
[page 1] Cover all cut cable ends that are not immediately
terminated to protect them from the weather and the entry
of foreign matter. Seal and repressurize air-dielectric
cable cable to prevent moisture from developing inside
the cable. Use the cable end caps that were supplied with
the cable shipment to cover the cable ends.
[page 7] Pressurization is needed in air-dielectric cables because
changes in temperature can cause condensation of
moisture from outside air that enters the cable. This
moisture can seriously impair the efficiency of system
operation. Connecting a pressure source of dry air or
nitrogen (dehydrator) to the cable at slightly more than
atmospheric pressure will correct this condition since
the moisture will be removed and air will then leak from
instead of into the cable.