diff --git a/src/Analyser/MutatingScope.php b/src/Analyser/MutatingScope.php
index 8bdf7894e6..69ab471021 100644
--- a/src/Analyser/MutatingScope.php
+++ b/src/Analyser/MutatingScope.php
@@ -1921,7 +1921,7 @@ public function resolveTypeByName(Name $name): TypeWithClassName
 		return new ObjectType($originalClass);
 	}
 
-	private function resolveTypeByNameWithLateStaticBinding(Name $class, Node\Identifier $name): TypeWithClassName
+	public function resolveTypeByNameWithLateStaticBinding(Name $class, Node\Identifier $name): TypeWithClassName
 	{
 		$classType = $this->resolveTypeByName($class);
 
diff --git a/src/Analyser/NodeScopeResolver.php b/src/Analyser/NodeScopeResolver.php
index bb361d5615..3c8ccdee17 100644
--- a/src/Analyser/NodeScopeResolver.php
+++ b/src/Analyser/NodeScopeResolver.php
@@ -3296,7 +3296,9 @@ function (MutatingScope $scope) use ($stmt, $expr, $nodeCallback, $context, $sto
 			}
 
 			$parametersAcceptor = null;
+			$classType = null;
 			$methodReflection = null;
+			$methodName = null;
 			if ($expr->name instanceof Expr) {
 				$result = $this->processExprNode($stmt, $expr->name, $scope, $storage, $nodeCallback, $context->enterDeep());
 				$hasYield = $hasYield || $result->hasYield();
@@ -3306,6 +3308,15 @@ function (MutatingScope $scope) use ($stmt, $expr, $nodeCallback, $context, $sto
 			} elseif ($expr->class instanceof Name) {
 				$classType = $scope->resolveTypeByName($expr->class);
 				$methodName = $expr->name->name;
+			} elseif ($expr->class instanceof Expr) {
+				$objectClasses = TypeCombinator::removeNull($scope->getType($expr->class))->getObjectTypeOrClassStringObjectType()->getObjectClassNames();
+				if (count($objectClasses) === 1) {
+					$classType = $scope->resolveTypeByNameWithLateStaticBinding(new Name($objectClasses[0]), $expr->name);
+					$methodName = $expr->name->name;
+				}
+			}
+
+			if ($classType !== null && $methodName !== null) {
 				if ($classType->hasMethod($methodName)->yes()) {
 					$methodReflection = $classType->getMethod($methodName, $scope);
 					$parametersAcceptor = ParametersAcceptorSelector::selectFromArgs(
@@ -3410,6 +3421,7 @@ function (MutatingScope $scope) use ($stmt, $expr, $nodeCallback, $context, $sto
 
 			if (
 				$methodReflection !== null
+				&& $expr->class instanceof Name
 				&& (
 					(
 						!$methodReflection->isStatic()
@@ -3425,6 +3437,7 @@ function (MutatingScope $scope) use ($stmt, $expr, $nodeCallback, $context, $sto
 
 			if (
 				$methodReflection !== null
+				&& $expr->class instanceof Name
 				&& !$methodReflection->isStatic()
 				&& $methodReflection->getName() === '__construct'
 				&& $scopeFunction instanceof MethodReflection
diff --git a/tests/PHPStan/Analyser/nsrt/bug-5020.php b/tests/PHPStan/Analyser/nsrt/bug-5020.php
new file mode 100644
index 0000000000..cefd581368
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-5020.php
@@ -0,0 +1,52 @@
+<?php
+
+namespace Bug5020;
+
+use function PHPStan\Testing\assertType;
+
+interface ITransformer
+{
+	public static function Transform(string $theInput, bool &$theErrorEncountered): string;
+}
+
+class Transformer implements ITransformer
+{
+	public static function Transform(string $theInput, bool &$theErrorEncountered): string
+	{
+		if ($theInput === 'invalid') {
+			$theErrorEncountered = true;
+			return '';
+		}
+		return strtoupper(trim($theInput));
+	}
+}
+
+function testConstantStringStaticCall(): void
+{
+	$transformer = 'Bug5020\Transformer';
+	$input = ' asdasda asdasd ';
+	$error = false;
+	$output = $transformer::Transform($input, $error);
+	assertType('string', $output);
+	assertType('bool', $error);
+}
+
+function testDirectStaticCall(): void
+{
+	$input = ' asdasda asdasd ';
+	$error = false;
+	$output = Transformer::Transform($input, $error);
+	assertType('string', $output);
+	assertType('bool', $error);
+}
+
+function testClassStringStaticCall(): void
+{
+	/** @var class-string<ITransformer> $transformer */
+	$transformer = 'Bug5020\Transformer';
+	$input = ' asdasda asdasd ';
+	$error = false;
+	$output = $transformer::Transform($input, $error);
+	assertType('string', $output);
+	assertType('bool', $error);
+}
diff --git a/tests/PHPStan/Rules/Methods/data/static-method-call-statement-no-side-effects.php b/tests/PHPStan/Rules/Methods/data/static-method-call-statement-no-side-effects.php
index 9c4e984e42..8a21b6f47a 100644
--- a/tests/PHPStan/Rules/Methods/data/static-method-call-statement-no-side-effects.php
+++ b/tests/PHPStan/Rules/Methods/data/static-method-call-statement-no-side-effects.php
@@ -10,7 +10,7 @@ class Foo
 	public function doFoo(\DateTimeImmutable $dt)
 	{
 		DateTimeImmutable::createFromFormat('Y-m-d', '2019-07-24');
-		$dt::createFromFormat('Y-m-d', '2019-07-24');
+		$dt::createFromFormat('Y-m-d', '2019-07-24'); // method might be impure in DateTimeImmutable subclass
 	}
 
 }