Perform Skill vs Tool Proficiency

One of the biggest proud nails in the 5e ruleset is the overlap between the Perform skill and the various tool proficiencies in musical instruments. This isn't helped by the fact that the Bard is the character most likely to take either proficiency - and indeed is likely to have both.

There are a few possible ways to nail this one flat:

Option 1: Just Ignore It

As the name implies, you could just ignore it. This is especially attractive because, as noted, the character most likely to have the relevant proficiencies is the Bard, who is likely to have both. Moreover, the Bard is most likely to make the checks using their most favoured instrument, so they'll almost always both apply.

Option 2: Remove the Perform Skill

A second option is to remove the Perform skill entirely. Make 'singing' another tool proficiency (effectively, just another instrument), and likewise 'oratory', 'acting', and so on. The downside of this is that the lines between the various different 'tools' are not immediately obvious.

Option 3: Perform Trumps Everything

In "Xanathar's Guide to Everything", a mechanism has been added to allow characters to learn new tool (and language) proficiencies. However, no similar mechanism exists for skill proficiencies.

Therefore, there's an argument for treating the Perform skill as proficiency in all instruments. A character who doesn't want to expend one of their very limited skill proficiencies on that can choose to pick up an odd instrument here or there, but it's less efficient. (That feels somewhat unsatisfactory, but it would work.)

Option 4: You Need Both

Alternately, there's the argument that you should need both - if you're performing using a lute, you need to be proficient in both Perform and the Lute. If you're missing either, you don't get the bonus. (I would, however, argue that expertise should apply if you have it in any of the appropriate areas.)

The appeal of this is then that you can apply the same to language proficiencies and social skills (so you can only Persuade the orcs if you speak Orcish), which has a certain neatness to it. And it also feels right - I know only too well that simply playing an instrument reasonably well doesn't automatically imply you can do so under the pressure of an audience's gaze. But it is rather inefficient, especially since it applies only to one fairly narrow niche area.

Conclusion

On balance, I'm leaning towards solution #1 (that is, just ignore it), unless and until it bugs someone in the group. However, if the players were to demand a solution, I'd probably lean to solution #3. And, if I were writing a theoretical 6th edition, I'd go with #4.