diff --git a/tests/python_package_test/test_dask.py b/tests/python_package_test/test_dask.py
index 86bc064e0829..dae1a8338821 100644
--- a/tests/python_package_test/test_dask.py
+++ b/tests/python_package_test/test_dask.py
@@ -11,6 +11,7 @@
 from urllib.parse import urlparse
 
 import pytest
+from sklearn.metrics import accuracy_score, r2_score
 
 import lightgbm as lgb
 
@@ -75,6 +76,13 @@ def cluster2():
     dask_cluster.close()
 
 
+@pytest.fixture(scope='module')
+def cluster_three_workers():
+    dask_cluster = LocalCluster(n_workers=3, threads_per_worker=1, dashboard_address=None)
+    yield dask_cluster
+    dask_cluster.close()
+
+
 @pytest.fixture()
 def listen_port():
     listen_port.port += 10
@@ -1503,56 +1511,54 @@ def f(part):
 
 @pytest.mark.parametrize('task', tasks)
 @pytest.mark.parametrize('output', data_output)
-def test_training_succeeds_even_if_some_workers_do_not_have_any_data(task, output, cluster):
-    pytest.skip("skipping due to timeout issues discussed in https://github.com/microsoft/LightGBM/pull/5510")
+def test_training_succeeds_even_if_some_workers_do_not_have_any_data(task, output, cluster_three_workers):
     if task == 'ranking' and output == 'scipy_csr_matrix':
         pytest.skip('LGBMRanker is not currently tested on sparse matrices')
 
-    with Client(cluster) as client:
-        def collection_to_single_partition(collection):
-            """Merge the parts of a Dask collection into a single partition."""
-            if collection is None:
-                return
-            if isinstance(collection, da.Array):
-                return collection.rechunk(*collection.shape)
-            return collection.repartition(npartitions=1)
-
-        X, y, w, g, dX, dy, dw, dg = _create_data(
+    with Client(cluster_three_workers) as client:
+        _, y, _, _, dX, dy, dw, dg = _create_data(
             objective=task,
             output=output,
-            group=None
+            group=None,
+            n_samples=1_000,
+            chunk_size=200,
         )
 
         dask_model_factory = task_to_dask_factory[task]
-        local_model_factory = task_to_local_factory[task]
 
-        dX = collection_to_single_partition(dX)
-        dy = collection_to_single_partition(dy)
-        dw = collection_to_single_partition(dw)
-        dg = collection_to_single_partition(dg)
+        workers = list(client.scheduler_info()['workers'].keys())
+        assert len(workers) == 3
+        first_two_workers = workers[:2]
 
-        n_workers = len(client.scheduler_info()['workers'])
-        assert n_workers > 1
-        assert dX.npartitions == 1
+        dX = client.persist(dX, workers=first_two_workers)
+        dy = client.persist(dy, workers=first_two_workers)
+        dw = client.persist(dw, workers=first_two_workers)
+        wait([dX, dy, dw])
+
+        workers_with_data = set()
+        for coll in (dX, dy, dw):
+            for with_data in client.who_has(coll).values():
+                workers_with_data.update(with_data)
+                assert workers[2] not in with_data
+        assert len(workers_with_data) == 2
 
         params = {
             'time_out': 5,
             'random_state': 42,
-            'num_leaves': 10
+            'num_leaves': 10,
+            'n_estimators': 20,
         }
 
         dask_model = dask_model_factory(tree='data', client=client, **params)
         dask_model.fit(dX, dy, group=dg, sample_weight=dw)
         dask_preds = dask_model.predict(dX).compute()
-
-        local_model = local_model_factory(**params)
-        if task == 'ranking':
-            local_model.fit(X, y, group=g, sample_weight=w)
+        if task == 'regression':
+            score = r2_score(y, dask_preds)
+        elif task.endswith('classification'):
+            score = accuracy_score(y, dask_preds)
         else:
-            local_model.fit(X, y, sample_weight=w)
-        local_preds = local_model.predict(X)
-
-        assert assert_eq(dask_preds, local_preds)
+            score = spearmanr(dask_preds, y).correlation
+        assert score > 0.9
 
 
 @pytest.mark.parametrize('task', tasks)