That's a different sort of proof, the computer equivalent of social proof.
It's not as cryptographically strong as zero-knowledge proofs can be. Those 5 nodes could all be dishonest, unless you know they are not.
Whereas you don't have to trust a zero-knowledge prover at all. A dishonest prover will "always" be detected (for a definition of "always" similar to general cryptography, i.e. extreme probabilities). Zk proofs (of the type I'm using) are more like fancy hash functions, where there's one correct answer and no node-specific key. Unlike, say, TLS PKI where you have to obtain certificates and trust particular nodes. (There are sometimes keys in zk, called "trusted setup", but those keys are computed in distributed ceremonies and shared with everyone.)
That said, there are some interesting tricks, similar to your idea, for distributing a zk computation among nodes who cross-verify-and-prove each other's work without needing to trust each other, reducing the amount of work per node and perhaps latency.
You do need the social proof type as well in practice. The zk proofs assert some fact which may accompany data, and some clever networking protocols can build on that, like proofs of (recent) data availability. But for consensus protocols, the zk proofs don't tell you which of those facts everyone is collectively agreeing to. For that, comparing results is required.
In blockchains where the p2p networking is automated, typically there's an assumption that your node will find at least one honest node with respect to the consensus, or some small number, and their information will outweigh bad information from other nodes. While bootstrapping more honest nodes are required than later, when following a networking in its live state.
But there's always a possibility that a node is only able to connect to a coordinated group of dishonest nodes, especially if someone is hacking the network aroud the target node, e.g. by affecting the routers. That's called an eclipse attack.
Note: I keep talking about blockchains because you asked about PoW, and that's where a lot of the zk proof of execution and proof of data availability stuff is focused these days, and it's a natural fit when multiple nodes and networking get discussed. But there are many non-blockchain uses as well!