diff --git a/compiler/src/dotty/tools/dotc/printing/PlainPrinter.scala b/compiler/src/dotty/tools/dotc/printing/PlainPrinter.scala
index cec8570a7597..3b7d08e2525b 100644
--- a/compiler/src/dotty/tools/dotc/printing/PlainPrinter.scala
+++ b/compiler/src/dotty/tools/dotc/printing/PlainPrinter.scala
@@ -181,7 +181,7 @@ class PlainPrinter(_ctx: Context) extends Printer {
       case tp: ErrorType =>
         s"<error ${tp.msg.msg}>"
       case tp: WildcardType =>
-        if (tp.optBounds.exists) "(?" ~ toTextRHS(tp.bounds) ~ ")" else "?"
+        if (tp.optBounds.exists) "<?" ~ toTextRHS(tp.bounds) ~ ">" else "<?>"
       case NoType =>
         "<notype>"
       case NoPrefix =>
diff --git a/compiler/src/dotty/tools/dotc/transform/Erasure.scala b/compiler/src/dotty/tools/dotc/transform/Erasure.scala
index 71a10cf6eb20..0d227a22bb60 100644
--- a/compiler/src/dotty/tools/dotc/transform/Erasure.scala
+++ b/compiler/src/dotty/tools/dotc/transform/Erasure.scala
@@ -419,15 +419,17 @@ object Erasure {
 
     /** Check that Java statics and packages can only be used in selections.
       */
-    private def checkValue(tree: Tree, proto: Type)(implicit ctx: Context): tree.type = {
-      if (!proto.isInstanceOf[SelectionProto] && !proto.isInstanceOf[ApplyingProto]) {
-        val sym = tree.tpe.termSymbol
-        // The check is avoided inside Java compilation units because it always fails
-        // on the singleton type Module.type.
-        if ((sym is Flags.Package) || (sym.isAllOf(Flags.JavaModule) && !ctx.compilationUnit.isJava)) ctx.error(reporting.diagnostic.messages.JavaSymbolIsNotAValue(sym), tree.sourcePos)
-      }
+    private def checkValue(tree: Tree, proto: Type)(implicit ctx: Context): tree.type =
+      if (!proto.isInstanceOf[SelectionProto] && !proto.isInstanceOf[ApplyingProto]) then
+        checkValue(tree)
       tree
-    }
+
+    private def checkValue(tree: Tree)(using ctx: Context): Unit =
+      val sym = tree.tpe.termSymbol
+      if (sym is Flags.Package)
+         || (sym.isAllOf(Flags.JavaModule) && !ctx.compilationUnit.isJava)
+      then
+        ctx.error(reporting.diagnostic.messages.JavaSymbolIsNotAValue(sym), tree.sourcePos)
 
     private def checkNotErased(tree: Tree)(implicit ctx: Context): tree.type = {
       if (!ctx.mode.is(Mode.Type)) {
@@ -551,6 +553,8 @@ object Erasure {
       val sym = if (owner eq origSym.maybeOwner) origSym else owner.info.decl(tree.name).symbol
       assert(sym.exists, origSym.showLocated)
 
+      if owner == defn.ObjectClass then checkValue(qual1)
+
       def select(qual: Tree, sym: Symbol): Tree =
         untpd.cpy.Select(tree)(qual, sym.name).withType(NamedType(qual.tpe, sym))
 
diff --git a/compiler/test/dotty/tools/dotc/reporting/ErrorMessagesTests.scala b/compiler/test/dotty/tools/dotc/reporting/ErrorMessagesTests.scala
index e1c017ad161c..f5c280ae290e 100644
--- a/compiler/test/dotty/tools/dotc/reporting/ErrorMessagesTests.scala
+++ b/compiler/test/dotty/tools/dotc/reporting/ErrorMessagesTests.scala
@@ -984,22 +984,6 @@ class ErrorMessagesTests extends ErrorMessagesTest {
       assertEquals(err, ImplicitClassPrimaryConstructorArity())
     }
 
-  @Test def anonymousFunctionMissingParamType =
-    checkMessagesAfter(RefChecks.name) {
-      """
-        |object AnonymousF {
-        |  val f = { case x: Int => x + 1 }
-        |}""".stripMargin
-    }
-    .expect { (ictx, messages) =>
-      implicit val ctx: Context = ictx
-
-      assertMessageCount(1, messages)
-      val AnonymousFunctionMissingParamType(param, args, _, pt) = messages.head
-      assertEquals("x$1", param.show)
-      assertEquals("?", pt.show)
-    }
-
   @Test def superCallsNotAllowedInline =
   checkMessagesAfter(RefChecks.name) {
        """
diff --git a/tests/neg/i5313.scala b/tests/neg/i5313.scala
new file mode 100644
index 000000000000..0add1d02dc58
--- /dev/null
+++ b/tests/neg/i5313.scala
@@ -0,0 +1,6 @@
+def test =
+  System.getClass  // error
+  System.toString  // error
+  System == null  // error
+  System eq null  // error
+  System.wait()  // error