Update package:vm_service dependency (#1334)

diff --git a/pkgs/test/CHANGELOG.md b/pkgs/test/CHANGELOG.md
index 810b8c7..9406b97 100644
--- a/pkgs/test/CHANGELOG.md
+++ b/pkgs/test/CHANGELOG.md
@@ -1,3 +1,7 @@
+## 1.16.0-nullsafety.4
+
+* Depend on the latest test_core.
+
 ## 1.16.0-nullsafety.3
 
 * Clean up `--help` output.
diff --git a/pkgs/test/pubspec.yaml b/pkgs/test/pubspec.yaml
index 09cf166..7478b92 100644
--- a/pkgs/test/pubspec.yaml
+++ b/pkgs/test/pubspec.yaml
@@ -1,5 +1,5 @@
 name: test
-version: 1.16.0-nullsafety.3
+version: 1.16.0-nullsafety.4
 description: A full featured library for writing and running Dart tests.
 homepage: https://github.com/dart-lang/test/blob/master/pkgs/test
 
@@ -34,7 +34,7 @@
   yaml: ^2.0.0
   # Use an exact version until the test_api and test_core package are stable.
   test_api: 0.2.19-nullsafety
-  test_core: 0.3.12-nullsafety.3
+  test_core: 0.3.12-nullsafety.4
 
 dev_dependencies:
   fake_async: ^1.0.0
diff --git a/pkgs/test_core/CHANGELOG.md b/pkgs/test_core/CHANGELOG.md
index 36c4c05..3bdc7a3 100644
--- a/pkgs/test_core/CHANGELOG.md
+++ b/pkgs/test_core/CHANGELOG.md
@@ -1,3 +1,7 @@
+## 0.3.12-nullsafety.4
+
+* Support latest `package:vm_service`.
+
 ## 0.3.12-nullsafety.3
 
 * Clean up `--help` output.
diff --git a/pkgs/test_core/pubspec.yaml b/pkgs/test_core/pubspec.yaml
index f383b39..20b3c88 100644
--- a/pkgs/test_core/pubspec.yaml
+++ b/pkgs/test_core/pubspec.yaml
@@ -1,5 +1,5 @@
 name: test_core
-version: 0.3.12-nullsafety.3
+version: 0.3.12-nullsafety.4
 description: A basic library for writing tests and running them on the VM.
 homepage: https://github.com/dart-lang/test/blob/master/pkgs/test_core
 
@@ -26,7 +26,7 @@
   source_span: '>=1.8.0-nullsafety <1.8.0'
   stack_trace: '>=1.10.0-nullsafety <1.10.0'
   stream_channel: ">=2.1.0-nullsafety <2.1.0"
-  vm_service: '>=1.0.0 <5.0.0'
+  vm_service: '>=1.0.0 <6.0.0'
   yaml: ^2.0.0
   # matcher is tightly constrained by test_api
   matcher: any