Yes, there is indeed a conflict, often described as a balancing act. Similarly, the principle of free speech protected by the First Amendment requires that the public tolerate lies in political rhetoric, and hateful public speech and insults, but can be balanced against an individual's interest in reputation in a libel case. See Near vs Minnesota and NY Times vs Sullivan for leading cases on this issue. There is also tension between the right of a newspaper to report on a current criminal case again under the First Amendment, and the defendant's Sixth Amendment right to a fair trial before an unbiased jury, which might be influenced by newspaper publicity.
In these and similar situations, there is no way to fully serve both protected interests, and courts must strike a balance and prefer one right over another, or find some compromise.
In the 5th vs 6th situation, courts have mostly favored the 5th. That is, the court will not require a witness to give up the right not to self-incriminate, and usually will not grant a defendant an acquittal because desired testimony is unavailable.
It might be that a defendant expected to rely on the testimony of a witness who has since died, or has fled the country and cannot be brought before the court. The sixth does not and cannot assure perfect justice, and the courts do not attempt to make it do so.
In the situation described, the defendant may compel the witness to appear and be asked the relevant questions. The jury will hear the answer, and may assume what it would have been without the invocation of the Fifth. The defendant's lawyer can try to find a question that the witness will answer, and can argue that the refusal to answer is consistent with a not-guilty verdict. That is all that the courts provide.
When the prosecution calls a witness, knowing or having good reason to know that the witness will invoke the 5th on more or less every relevant question, the US Supreme Court in Namet v. United States 373 U.S. 179 (1963) has held that this may be error requiring overturning the conviction. This was confirmed and expanded in Douglas v. Alabama 380 U.S. 415 (1965). But neither of these are relevant when the defense calls the witness.