diff --git a/core/engine/src/bytecompiler/class.rs b/core/engine/src/bytecompiler/class.rs
index 9e7a00190f2..0031f2b4e35 100644
--- a/core/engine/src/bytecompiler/class.rs
+++ b/core/engine/src/bytecompiler/class.rs
@@ -207,16 +207,6 @@ impl ByteCompiler<'_> {
 
         let mut static_elements = Vec::new();
 
-        if let Some(scope) = class.name_scope {
-            let binding = scope.get_identifier_reference(class_name.clone());
-            let index = self.insert_binding(binding);
-            self.emit_binding_access(
-                BindingAccessOpcode::PutLexicalValue,
-                &index,
-                &class_register,
-            );
-        }
-
         for element in class.elements {
             match element {
                 ClassElement::MethodDefinition(m) => match m.name() {
@@ -505,6 +495,10 @@ impl ByteCompiler<'_> {
                         PropertyName::Computed(name) => {
                             let name_register = self.register_allocator.alloc();
                             self.compile_expr(name, &name_register);
+                            self.bytecode.emit_to_property_key(
+                                name_register.variable(),
+                                name_register.variable(),
+                            );
                             StaticFieldName::Register(name_register)
                         }
                     };
@@ -635,6 +629,19 @@ impl ByteCompiler<'_> {
             }
         }
 
+        // ClassDefinitionEvaluation initializes the class binding after evaluating
+        // all element names, but before executing static initializers.
+        // https://tc39.es/ecma262/#sec-runtime-semantics-classdefinitionevaluation
+        if let Some(scope) = class.name_scope {
+            let binding = scope.get_identifier_reference(class_name.clone());
+            let index = self.insert_binding(binding);
+            self.emit_binding_access(
+                BindingAccessOpcode::PutLexicalValue,
+                &index,
+                &class_register,
+            );
+        }
+
         for element in static_elements {
             match element {
                 StaticElement::StaticBlock(code) => {
@@ -682,8 +689,6 @@ impl ByteCompiler<'_> {
                         }
                         StaticFieldName::Register(key) => {
                             if is_anonymous_function {
-                                self.bytecode
-                                    .emit_to_property_key(key.variable(), key.variable());
                                 self.bytecode.emit_set_function_name(
                                     value.variable(),
                                     key.variable(),
diff --git a/core/engine/src/tests/class.rs b/core/engine/src/tests/class.rs
index 98e3845f86f..aed00713dc5 100644
--- a/core/engine/src/tests/class.rs
+++ b/core/engine/src/tests/class.rs
@@ -2,6 +2,99 @@ use crate::{TestAction, run_test_actions};
 use boa_macros::js_str;
 use indoc::indoc;
 
+// https://github.com/boa-dev/boa/issues/5635
+#[test]
+fn computed_class_field_keys_follow_source_order() {
+    run_test_actions([
+        TestAction::run(indoc! {r#"
+            let n = 0;
+            const key = { toString() { return "k" + ++n; } };
+            class C {
+                [key]() { return 1; }
+                static [key] = 2;
+                [key] = 3;
+            }
+            const instance = new C();
+        "#}),
+        TestAction::assert_eq("instance.k1()", 1),
+        TestAction::assert_eq("C.k2", 2),
+        TestAction::assert_eq("instance.k3", 3),
+        TestAction::assert_eq("n", 3),
+    ]);
+}
+
+#[test]
+fn computed_static_field_key_precedes_initializers() {
+    run_test_actions([
+        TestAction::run(indoc! {r#"
+            const events = [];
+            const key = {
+                toString() {
+                    events.push("key");
+                    return "field";
+                }
+            };
+            class C {
+                static first = events.push("first");
+                static [key] = events.push("second");
+            }
+        "#}),
+        TestAction::assert_eq("events.join(',')", js_str!("key,first,second")),
+        TestAction::assert_eq("C.field", 3),
+    ]);
+}
+
+#[test]
+fn abrupt_computed_static_field_key_prevents_initializers() {
+    run_test_actions([
+        TestAction::run("let initialized = false;"),
+        TestAction::assert_opaque_error(
+            indoc! {r#"
+                class C {
+                    static first = (initialized = true);
+                    static [{ toString() { throw "key"; } }] = 1;
+                }
+            "#},
+            js_str!("key"),
+        ),
+        TestAction::assert("!initialized"),
+    ]);
+}
+
+#[test]
+fn class_name_is_uninitialized_in_computed_keys() {
+    for source in [
+        "class C { [C] = 1; }",
+        "class C { static [C] = 1; }",
+        "class C { [C]() {} }",
+        "(class C { [C] = 1; });",
+        "(class C { static [C] = 1; });",
+        "(class C { [C]() {} });",
+    ] {
+        run_test_actions([TestAction::assert_native_error(
+            source,
+            crate::JsNativeErrorKind::Reference,
+            "C is not defined",
+        )]);
+    }
+}
+
+#[test]
+fn class_name_is_initialized_before_static_initializers() {
+    run_test_actions([
+        TestAction::run(indoc! {r#"
+            class C {
+                static self = C;
+                static { this.matches = C === this; }
+                self = C;
+            }
+        "#}),
+        TestAction::assert("C.self === C"),
+        TestAction::assert("C.matches"),
+        TestAction::assert("new C().self === C"),
+    ]);
+}
+
 #[test]
 fn class_field_initializer_name_static() {
     run_test_actions([