Does the invocation of the 5th amendment ever constitute evidence of having committed a crime?
I haven't found a recent case like this where it constitutes evidence.
Military members didn't have an express right to remain silent until somewhere in the 1950s, so one chances are there might be cases prior to that point. The present right is codified in 10 U.S.C. 831, which is Article 31 of the UCMJ.
That said, there is certainly a well documented adverse inference effect. While jurors aren't supposed to take the silence into account (e.g. when a defendant elects not to testify or exercises a right against self-incrimination), it's a difficult thing to do, practically speaking.
From the point of view of another jurisdiction; Australia does not have a statutory or constitutional right against self-incrimination, however, such a right is recognised in the common law.
Juries are specifically permitted to draw inferences from silence where the defendant is in the position to know material facts that are not otherwise in evidence. For example, there was a Queensland case (name escapes me for the moment) where the facts were that a husband and wife had hired the defendant as a deck-hand on their yacht and sailed into the South Pacific. No further news was heard of the couple but the defendant and the yacht turned up without them whereupon the defendant was charged with their murder, tried and convicted. The trial judge instructed the jury that they could draw inference from the defendant's silence when he was clearly in a position to know what happened and chose not to offer any explanation. The court of appeal held that the direction was OK.