diff --git a/test_runner/performance/test_wal_backpressure.py b/test_runner/performance/test_wal_backpressure.py
index 3939ca30b6..3cb4b667ff 100644
--- a/test_runner/performance/test_wal_backpressure.py
+++ b/test_runner/performance/test_wal_backpressure.py
@@ -65,7 +65,7 @@ def start_heavy_write_workload(env: PgCompare, n_tables: int, scale: int, num_it
 
     def start_single_table_workload(table_id: int):
         for _ in range(num_iters):
-            with env.pg.connect().cursor() as cur:
+            with env.pg.connect(options="-cstatement_timeout=300s").cursor() as cur:
                 cur.execute(
                     f"INSERT INTO t{table_id} SELECT FROM generate_series(1,{new_rows_each_update})"
                 )
diff --git a/test_runner/regress/test_wal_acceptor_async.py b/test_runner/regress/test_wal_acceptor_async.py
index cfc131a3aa..81a2411271 100644
--- a/test_runner/regress/test_wal_acceptor_async.py
+++ b/test_runner/regress/test_wal_acceptor_async.py
@@ -6,6 +6,7 @@ from pathlib import Path
 from typing import List, Optional
 
 import asyncpg
+import pytest
 import toml
 from fixtures.log_helper import getLogger
 from fixtures.neon_fixtures import Endpoint, NeonEnv, NeonEnvBuilder, Safekeeper
@@ -597,7 +598,10 @@ async def run_wal_lagging(env: NeonEnv, endpoint: Endpoint, test_output_dir: Pat
     assert res == expected_sum
 
 
-# do inserts while restarting postgres and messing with safekeeper addresses
+# Do inserts while restarting postgres and messing with safekeeper addresses.
+# The test takes more than default 5 minutes on Postgres 16,
+# see https://github.com/neondatabase/neon/issues/5305
+@pytest.mark.timeout(600)
 def test_wal_lagging(neon_env_builder: NeonEnvBuilder, test_output_dir: Path):
     neon_env_builder.num_safekeepers = 3
     env = neon_env_builder.init_start()