diff --git a/package.json b/package.json
index 7d9999d76..0fd3b1d4e 100644
--- a/package.json
+++ b/package.json
@@ -79,7 +79,7 @@
     ]
   },
   "dependencies": {
-    "@typescript-eslint/experimental-utils": "^4.0.1"
+    "@typescript-eslint/experimental-utils": "^5.0.0"
   },
   "devDependencies": {
     "@babel/cli": "^7.4.4",
diff --git a/src/index.ts b/src/index.ts
index b105f3db4..0bed30e16 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -8,11 +8,10 @@ type RuleModule = TSESLint.RuleModule<string, unknown[]> & {
   meta: Required<Pick<TSESLint.RuleMetaData<string>, 'docs'>>;
 };
 
-// can be removed once we've on v5 of `@typescript-eslint/experimental-utils`
+// v5 of `@typescript-eslint/experimental-utils` removed this
 declare module '@typescript-eslint/experimental-utils/dist/ts-eslint/Rule' {
-  // eslint-disable-next-line @typescript-eslint/no-unused-vars
-  export interface RuleMetaData<TMessageIds extends string> {
-    hasSuggestions?: boolean;
+  export interface RuleMetaDataDocs {
+    category: 'Best Practices' | 'Possible Errors';
   }
 }
 
diff --git a/src/rules/utils.ts b/src/rules/utils.ts
index 0e946b4a2..320b73140 100644
--- a/src/rules/utils.ts
+++ b/src/rules/utils.ts
@@ -681,7 +681,7 @@ const isTestCaseName = (node: TSESTree.LeftHandSideExpression) =>
   TestCaseName.hasOwnProperty(node.name);
 
 const isTestCaseProperty = (
-  node: TSESTree.Expression,
+  node: TSESTree.Expression | TSESTree.PrivateIdentifier,
 ): node is AccessorNode<TestCaseProperty> =>
   isSupportedAccessor(node) &&
   TestCaseProperty.hasOwnProperty(getAccessorValue(node));
@@ -737,7 +737,7 @@ const isDescribeAlias = (node: TSESTree.LeftHandSideExpression) =>
   DescribeAlias.hasOwnProperty(node.name);
 
 const isDescribeProperty = (
-  node: TSESTree.Expression,
+  node: TSESTree.Expression | TSESTree.PrivateIdentifier,
 ): node is AccessorNode<DescribeProperty> =>
   isSupportedAccessor(node) &&
   DescribeProperty.hasOwnProperty(getAccessorValue(node));
diff --git a/yarn.lock b/yarn.lock
index 493c9fb50..dd8fc2d6b 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -2544,7 +2544,7 @@ __metadata:
   languageName: node
   linkType: hard
 
-"@typescript-eslint/experimental-utils@npm:4.33.0, @typescript-eslint/experimental-utils@npm:^4.0.1, @typescript-eslint/experimental-utils@npm:^4.11.1":
+"@typescript-eslint/experimental-utils@npm:4.33.0, @typescript-eslint/experimental-utils@npm:^4.11.1":
   version: 4.33.0
   resolution: "@typescript-eslint/experimental-utils@npm:4.33.0"
   dependencies:
@@ -2560,6 +2560,22 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@typescript-eslint/experimental-utils@npm:^5.0.0":
+  version: 5.0.0
+  resolution: "@typescript-eslint/experimental-utils@npm:5.0.0"
+  dependencies:
+    "@types/json-schema": ^7.0.7
+    "@typescript-eslint/scope-manager": 5.0.0
+    "@typescript-eslint/types": 5.0.0
+    "@typescript-eslint/typescript-estree": 5.0.0
+    eslint-scope: ^5.1.1
+    eslint-utils: ^3.0.0
+  peerDependencies:
+    eslint: "*"
+  checksum: 0c545cf353b225460d37d9ff99b798db9ed83a5446457f54a79309938e5068799fd9a565c1f964d734e45a91b4bdd52db77ae5063e2d669ef5f7603f14fbb43c
+  languageName: node
+  linkType: hard
+
 "@typescript-eslint/parser@npm:^4.0.1":
   version: 4.33.0
   resolution: "@typescript-eslint/parser@npm:4.33.0"
@@ -2587,6 +2603,16 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@typescript-eslint/scope-manager@npm:5.0.0":
+  version: 5.0.0
+  resolution: "@typescript-eslint/scope-manager@npm:5.0.0"
+  dependencies:
+    "@typescript-eslint/types": 5.0.0
+    "@typescript-eslint/visitor-keys": 5.0.0
+  checksum: 920fc3553830c738d2d709676d95e50f7b0fe945afad0457527753e94e3ac115b6c88f1974eecc9bcb6d9580373250fa36765484fee45b4513bd4f63eceaa6a3
+  languageName: node
+  linkType: hard
+
 "@typescript-eslint/types@npm:4.33.0":
   version: 4.33.0
   resolution: "@typescript-eslint/types@npm:4.33.0"
@@ -2594,6 +2620,13 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@typescript-eslint/types@npm:5.0.0":
+  version: 5.0.0
+  resolution: "@typescript-eslint/types@npm:5.0.0"
+  checksum: 424966c124cd02b8d8bebe3ae4fb264e23708018e6e63787a070ced1bb24c43c4e3b49adb895eaf9a8200bed5c97aa7a57a1605925b6fb56a091703648e29b40
+  languageName: node
+  linkType: hard
+
 "@typescript-eslint/typescript-estree@npm:4.33.0":
   version: 4.33.0
   resolution: "@typescript-eslint/typescript-estree@npm:4.33.0"
@@ -2612,6 +2645,24 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@typescript-eslint/typescript-estree@npm:5.0.0":
+  version: 5.0.0
+  resolution: "@typescript-eslint/typescript-estree@npm:5.0.0"
+  dependencies:
+    "@typescript-eslint/types": 5.0.0
+    "@typescript-eslint/visitor-keys": 5.0.0
+    debug: ^4.3.1
+    globby: ^11.0.3
+    is-glob: ^4.0.1
+    semver: ^7.3.5
+    tsutils: ^3.21.0
+  peerDependenciesMeta:
+    typescript:
+      optional: true
+  checksum: 950e72b75706fa75dd795f3bbd29222a9da5c611f0acc023bf82f3254476fbdb3bfe0a07aa75105f2c2bfe566191f9125351cdf003be4a1fe6a5ee8bd1cd2dc7
+  languageName: node
+  linkType: hard
+
 "@typescript-eslint/visitor-keys@npm:4.33.0":
   version: 4.33.0
   resolution: "@typescript-eslint/visitor-keys@npm:4.33.0"
@@ -2622,6 +2673,16 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@typescript-eslint/visitor-keys@npm:5.0.0":
+  version: 5.0.0
+  resolution: "@typescript-eslint/visitor-keys@npm:5.0.0"
+  dependencies:
+    "@typescript-eslint/types": 5.0.0
+    eslint-visitor-keys: ^3.0.0
+  checksum: 6a5a3cdd64d9b131c72aa52f44904b5bb0fbb28ca624342afdfafa9dd0038f2de9a02ed661595ddb2c8133ab0854b320fb0d1c9d9823c7c064663d506f8c1d4a
+  languageName: node
+  linkType: hard
+
 "JSONStream@npm:^1.0.4":
   version: 1.3.5
   resolution: "JSONStream@npm:1.3.5"
@@ -4409,7 +4470,7 @@ __metadata:
     "@types/node": ^14.0.0
     "@types/prettier": ^2.0.0
     "@typescript-eslint/eslint-plugin": ^4.0.1
-    "@typescript-eslint/experimental-utils": ^4.0.1
+    "@typescript-eslint/experimental-utils": ^5.0.0
     "@typescript-eslint/parser": ^4.0.1
     babel-jest: ^27.0.0
     babel-plugin-replace-ts-export-assignment: ^0.0.2
@@ -4519,6 +4580,13 @@ __metadata:
   languageName: node
   linkType: hard
 
+"eslint-visitor-keys@npm:^3.0.0":
+  version: 3.0.0
+  resolution: "eslint-visitor-keys@npm:3.0.0"
+  checksum: 352607f367a2e0e2f9f234e40d6d9b34c39399345b8a9f204e1343749ddfae505d8343909cba6c4abc2ca03add4cdc0530af5e98f870ad7183fc2a89458669e5
+  languageName: node
+  linkType: hard
+
 "eslint@npm:^6.0.0 || ^7.0.0":
   version: 7.32.0
   resolution: "eslint@npm:7.32.0"