diff --git a/clippy_lints/src/utils/mod.rs b/clippy_lints/src/utils/mod.rs
index 820052571156..fe2ee0931573 100644
--- a/clippy_lints/src/utils/mod.rs
+++ b/clippy_lints/src/utils/mod.rs
@@ -899,7 +899,7 @@ pub fn is_ctor_or_promotable_const_function(cx: &LateContext<'_>, expr: &Expr<'_
             return match res {
                 def::Res::Def(DefKind::Variant | DefKind::Ctor(..), ..) => true,
                 // FIXME: check the constness of the arguments, see https://github.com/rust-lang/rust-clippy/pull/5682#issuecomment-638681210
-                def::Res::Def(DefKind::Fn, def_id) if has_no_arguments(cx, def_id) => {
+                def::Res::Def(DefKind::Fn | DefKind::AssocFn, def_id) if has_no_arguments(cx, def_id) => {
                     const_eval::is_const_fn(cx.tcx, def_id)
                 },
                 def::Res::Def(_, def_id) => cx.tcx.is_promotable_const_fn(def_id),
diff --git a/tests/ui/or_fun_call.fixed b/tests/ui/or_fun_call.fixed
index 67faa8bd4a0a..5fb568672d35 100644
--- a/tests/ui/or_fun_call.fixed
+++ b/tests/ui/or_fun_call.fixed
@@ -58,12 +58,6 @@ fn or_fun_call() {
     let without_default = Some(Foo);
     without_default.unwrap_or_else(Foo::new);
 
-    let mut map = HashMap::<u64, String>::new();
-    map.entry(42).or_insert_with(String::new);
-
-    let mut btree = BTreeMap::<u64, String>::new();
-    btree.entry(42).or_insert_with(String::new);
-
     let stringy = Some(String::from(""));
     let _ = stringy.unwrap_or_else(|| "".to_owned());
 
@@ -122,6 +116,17 @@ pub fn skip_const_fn_with_no_args() {
         Some(42)
     }
     let _ = None.or(foo());
+
+    // See issue #5693.
+    let mut map = std::collections::HashMap::new();
+    map.insert(1, vec![1]);
+    map.entry(1).or_insert(vec![]);
+
+    let mut map = HashMap::<u64, String>::new();
+    map.entry(42).or_insert(String::new());
+
+    let mut btree = BTreeMap::<u64, String>::new();
+    btree.entry(42).or_insert(String::new());
 }
 
 fn main() {}
diff --git a/tests/ui/or_fun_call.rs b/tests/ui/or_fun_call.rs
index 9867e2eedcff..737b0f7e55bc 100644
--- a/tests/ui/or_fun_call.rs
+++ b/tests/ui/or_fun_call.rs
@@ -58,12 +58,6 @@ fn or_fun_call() {
     let without_default = Some(Foo);
     without_default.unwrap_or(Foo::new());
 
-    let mut map = HashMap::<u64, String>::new();
-    map.entry(42).or_insert(String::new());
-
-    let mut btree = BTreeMap::<u64, String>::new();
-    btree.entry(42).or_insert(String::new());
-
     let stringy = Some(String::from(""));
     let _ = stringy.unwrap_or("".to_owned());
 
@@ -122,6 +116,17 @@ pub fn skip_const_fn_with_no_args() {
         Some(42)
     }
     let _ = None.or(foo());
+
+    // See issue #5693.
+    let mut map = std::collections::HashMap::new();
+    map.insert(1, vec![1]);
+    map.entry(1).or_insert(vec![]);
+
+    let mut map = HashMap::<u64, String>::new();
+    map.entry(42).or_insert(String::new());
+
+    let mut btree = BTreeMap::<u64, String>::new();
+    btree.entry(42).or_insert(String::new());
 }
 
 fn main() {}
diff --git a/tests/ui/or_fun_call.stderr b/tests/ui/or_fun_call.stderr
index bc5978b538f1..b8a436993f32 100644
--- a/tests/ui/or_fun_call.stderr
+++ b/tests/ui/or_fun_call.stderr
@@ -60,35 +60,23 @@ error: use of `unwrap_or` followed by a function call
 LL |     without_default.unwrap_or(Foo::new());
    |                     ^^^^^^^^^^^^^^^^^^^^^ help: try this: `unwrap_or_else(Foo::new)`
 
-error: use of `or_insert` followed by a function call
-  --> $DIR/or_fun_call.rs:62:19
-   |
-LL |     map.entry(42).or_insert(String::new());
-   |                   ^^^^^^^^^^^^^^^^^^^^^^^^ help: try this: `or_insert_with(String::new)`
-
-error: use of `or_insert` followed by a function call
-  --> $DIR/or_fun_call.rs:65:21
-   |
-LL |     btree.entry(42).or_insert(String::new());
-   |                     ^^^^^^^^^^^^^^^^^^^^^^^^ help: try this: `or_insert_with(String::new)`
-
 error: use of `unwrap_or` followed by a function call
-  --> $DIR/or_fun_call.rs:68:21
+  --> $DIR/or_fun_call.rs:62:21
    |
 LL |     let _ = stringy.unwrap_or("".to_owned());
    |                     ^^^^^^^^^^^^^^^^^^^^^^^^ help: try this: `unwrap_or_else(|| "".to_owned())`
 
 error: use of `or` followed by a function call
-  --> $DIR/or_fun_call.rs:93:35
+  --> $DIR/or_fun_call.rs:87:35
    |
 LL |     let _ = Some("a".to_string()).or(Some("b".to_string()));
    |                                   ^^^^^^^^^^^^^^^^^^^^^^^^^ help: try this: `or_else(|| Some("b".to_string()))`
 
 error: use of `or` followed by a function call
-  --> $DIR/or_fun_call.rs:97:10
+  --> $DIR/or_fun_call.rs:91:10
    |
 LL |         .or(Some(Bar(b, Duration::from_secs(2))));
    |          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ help: try this: `or_else(|| Some(Bar(b, Duration::from_secs(2))))`
 
-error: aborting due to 15 previous errors
+error: aborting due to 13 previous errors