The pattern can work, but the domain matters, the test type matters (unit, integration, ui) and the trade-off associated matter.
e.g. If I am running a long-running UI-test scenario, I absolutely don't want test-5 to walk through 80% of the UI that was already exercised in tests 1-4. I am creating test coupling, but I'm saving cost/time by doing so.
But, you'll also hear why not to do this, because it creates test coupling / breaks atomic tests, which is generally seen as bad.
If that is a local integration test and those early steps run is millis? Then maybe we keep things uncoupled to allow the system to exercise the pathways without explicit expectations.