You just can’t stop nerds from inventing a new voting system every time they have to vote .
The “if there are 5 ultimate winners, vote for at most 5” scheme is an instance of what’s called “first past the post bloc voting” here. As that brief article implies, at least in the presence of political factions it sucks for the same basic reasons the “first past the post” (plurality) single-winner scheme sucks: because the number you can vote for is limited, the pressure is high not to vote for your true favorite(s) if you guess they can’t win, but people who vote for doomed true favorites anyway can “split the vote”. The vote(s) they “waste” voting for the doomed are votes that may be taken away from what would otherwise have been consensus winners.
But neither approval nor Condorcet were designed with multiple winners in mind either. The specific Ranked Pairs Condorcet method was designed to produce a total ordering (which is, indeed, Schulze’s complaint about it: Schulze only cares about single-winner elections, and optimizing for a total ordering may not produce the same choice in the #1 spot as optimizing for a single winner).
But in the absence of political factions, there’s really little to object to in plain Approval (approve of as many or as few as you like) voting for a multi-winner election. That’s why David Mertz pushed it through for PSF Board elections long ago. And it remains an improvement over its successors so far .
Highly regarded multi-winner systems in the presence of political factions involve all sorts of complications to ensure that a minority faction has a good chance of getting a share of winners roughly equal to that minority’s share of the electorate.
For example, in “reweighted range voting” everyone gives scores to candidates (approval voting is like that with the only scores allowed being 0 or 1). The candidate with the highest total (or average) score is one of the winners. Then every score on every ballot is effectively adjusted, so that ballots who rated the winner highly carry less weight for the next round (“you already got much of what you want, so let’s give minorities a chance too”). Lather, rinse, repeat.
But in the absence of that, you just can’t beat plain approval or range voting for simplicity and transparency. Limiting approval voting to at most 5 approvals in a 5-winner election is a Highly Dubious Idea on the face of it, according to me - gratuitous novelty.