diff --git a/pageserver/src/page_service.rs b/pageserver/src/page_service.rs
index be9782847b57..5193b3c5ff50 100644
--- a/pageserver/src/page_service.rs
+++ b/pageserver/src/page_service.rs
@@ -14,6 +14,7 @@ use async_compression::tokio::write::GzipEncoder;
 use bytes::Buf;
 use bytes::Bytes;
 use futures::Stream;
+use pageserver_api::models::TenantState;
 use pageserver_api::models::{
     PagestreamBeMessage, PagestreamDbSizeRequest, PagestreamDbSizeResponse,
     PagestreamErrorResponse, PagestreamExistsRequest, PagestreamExistsResponse,
@@ -1330,6 +1331,9 @@ impl From<GetActiveTenantError> for QueryError {
             GetActiveTenantError::WaitForActiveTimeout { .. } => QueryError::Disconnected(
                 ConnectionError::Io(io::Error::new(io::ErrorKind::TimedOut, e.to_string())),
             ),
+            GetActiveTenantError::WillNotBecomeActive(TenantState::Stopping { .. }) => {
+                QueryError::Shutdown
+            }
             e => QueryError::Other(anyhow::anyhow!(e)),
         }
     }
diff --git a/test_runner/regress/test_pageserver_restarts_under_workload.py b/test_runner/regress/test_pageserver_restarts_under_workload.py
index d07b8dbe6b7b..65569f3bac9e 100644
--- a/test_runner/regress/test_pageserver_restarts_under_workload.py
+++ b/test_runner/regress/test_pageserver_restarts_under_workload.py
@@ -17,10 +17,6 @@ def test_pageserver_restarts_under_worload(neon_simple_env: NeonEnv, pg_bin: PgB
     n_restarts = 10
     scale = 10
 
-    # Pageserver currently logs requests on non-active tenants at error level
-    # https://github.com/neondatabase/neon/issues/5784
-    env.pageserver.allowed_errors.append(".* will not become active. Current state: Stopping.*")
-
     def run_pgbench(connstr: str):
         log.info(f"Start a pgbench workload on pg {connstr}")
         pg_bin.run_capture(["pgbench", "-i", f"-s{scale}", connstr])