Include most Vulkan tests in ASAN build.
diff --git a/build_tools/cmake/test.sh b/build_tools/cmake/test.sh
index bb0c5c5..50d4640 100755
--- a/build_tools/cmake/test.sh
+++ b/build_tools/cmake/test.sh
@@ -18,8 +18,7 @@
 # Respect the user setting, but default to as many jobs as we have cores.
 export CTEST_PARALLEL_LEVEL=${CTEST_PARALLEL_LEVEL:-$(nproc)}
 
-# Respect the user setting, but default to turning off the vulkan tests
-# and turning on the llvmaot ones.
+# Respect the user setting, but default to turning on vulkan and llvmaot.
 export IREE_VULKAN_DISABLE=${IREE_VULKAN_DISABLE:-0}
 export IREE_LLVMAOT_DISABLE=${IREE_LLVMAOT_DISABLE:-0}
 # CUDA is off by default.
diff --git a/build_tools/kokoro/gcp_ubuntu/cmake/linux/x86-swiftshader-asan/build.sh b/build_tools/kokoro/gcp_ubuntu/cmake/linux/x86-swiftshader-asan/build.sh
index 0076da6..1e0826c 100755
--- a/build_tools/kokoro/gcp_ubuntu/cmake/linux/x86-swiftshader-asan/build.sh
+++ b/build_tools/kokoro/gcp_ubuntu/cmake/linux/x86-swiftshader-asan/build.sh
@@ -52,10 +52,8 @@
 # Respect the user setting, but default to as many jobs as we have cores.
 export CTEST_PARALLEL_LEVEL=${CTEST_PARALLEL_LEVEL:-$(nproc)}
 
-# Respect the user setting, but default to turning off the vulkan tests
-# and turning on the llvmaot ones.
-# TODO(#5716): Fix and enable Vulkan tests.
-export IREE_VULKAN_DISABLE=${IREE_VULKAN_DISABLE:-1}
+# Respect the user setting, but default to turning on vulkan and llvmaot.
+export IREE_VULKAN_DISABLE=${IREE_VULKAN_DISABLE:-0}
 export IREE_LLVMAOT_DISABLE=${IREE_LLVMAOT_DISABLE:-0}
 # CUDA is off by default.
 export IREE_CUDA_DISABLE=${IREE_CUDA_DISABLE:-1}
@@ -105,7 +103,11 @@
 # These tests currently have asan failures
 # TODO(#5715): Fix these
 declare -a excluded_tests=(
+  # Mysterious "LeakSanitizer has encountered a fatal error." crashes
   "iree/samples/simple_embedding/simple_embedding_vulkan_test"
+  "iree/tools/test/iree-benchmark-module.mlir.test"
+  "iree/tools/test/iree-run-module.mlir.test"
+  "iree/tools/test/multiple_exported_functions.mlir.test"
 )
 
 # Prefix with `^` anchor
@@ -120,5 +122,5 @@
 
 echo "Testing with ctest"
 ctest --timeout 900 --output-on-failure \
-  --label-exclude "^driver=cuda$|^driver=vulkan$" \
+  --label-exclude "${label_exclude_regex}" \
   --exclude-regex "${excluded_tests_regex?}"