The US 5"/38 caliber gun was a widely used weapon that equipped many ships of the US navy and was typically used in the dual capacity of engaging both surface and air targets.

Could this gun have served effectively in the roles of AA, artillery or even anti-tank?

In naval use it did see service in those capacities. As a ground weapon, probably not. For naval use weight was not an issue high on the list. The 5"/38, like many weapons, was a compromise between having a good surface action gun with high velocity and a flat trajectory and a good AA gun that had a high rate of fire and had a high elevation on a reasonable size and weight of mounting.
In this sense the 38 was better than the 5"/25 and 5"/51 that were in service previously in more or less single purpose roles of AA and surface respectively. In a land role it would have resulted in a mediocre design compared to what the US Army actually used. As an AA gun it would have been too heavy for good mobility. Note how the US didn't even use the available 120mm AA gun overseas due to this problem. As artillery its shell would offer little advantage over the much lighter 105mm howitzer and would have been worse than the 155mm howitzer. It couldn't match the 155 gun in range and would have proven little better than the 4.5" gun.
As an anti-tank weapon it would have been a monstrosity that offered poor performance on the whole and would have required being self-propelled to be of any real value.

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Truth is stranger than bullshit!

I would add that an essential requirement for an anti-tank gun is high velocity. This is not only because armour penetration depends on striking energy (which is strongly dependent on impact velocity), but also because it provides a flat trajectory and a short flight time, thereby maximising hit probability.

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Tony Williams: Military gun and ammunition website