diff --git a/tokio/src/runtime/time/entry.rs b/tokio/src/runtime/time/entry.rs
index 6aea2b15cb3..798d3c11eb8 100644
--- a/tokio/src/runtime/time/entry.rs
+++ b/tokio/src/runtime/time/entry.rs
@@ -72,6 +72,10 @@ type TimerResult = Result<(), crate::time::error::Error>;
 const STATE_DEREGISTERED: u64 = u64::MAX;
 const STATE_PENDING_FIRE: u64 = STATE_DEREGISTERED - 1;
 const STATE_MIN_VALUE: u64 = STATE_PENDING_FIRE;
+/// The largest safe integer to use for ticks.
+///
+/// This value should be updated if any other signal values are added above.
+pub(super) const MAX_SAFE_MILLIS_DURATION: u64 = u64::MAX - 2;
 
 /// This structure holds the current shared state of the timer - its scheduled
 /// time (if registered), or otherwise the result of the timer completing, as
@@ -126,7 +130,7 @@ impl StateCell {
     fn when(&self) -> Option<u64> {
         let cur_state = self.state.load(Ordering::Relaxed);
 
-        if cur_state == u64::MAX {
+        if cur_state == STATE_DEREGISTERED {
             None
         } else {
             Some(cur_state)
diff --git a/tokio/src/runtime/time/mod.rs b/tokio/src/runtime/time/mod.rs
index 215714dd576..423ad79ab91 100644
--- a/tokio/src/runtime/time/mod.rs
+++ b/tokio/src/runtime/time/mod.rs
@@ -8,7 +8,7 @@
 
 mod entry;
 pub(crate) use entry::TimerEntry;
-use entry::{EntryList, TimerHandle, TimerShared};
+use entry::{EntryList, TimerHandle, TimerShared, MAX_SAFE_MILLIS_DURATION};
 
 mod handle;
 pub(crate) use self::handle::Handle;
diff --git a/tokio/src/runtime/time/source.rs b/tokio/src/runtime/time/source.rs
index 412812da193..4647bc41223 100644
--- a/tokio/src/runtime/time/source.rs
+++ b/tokio/src/runtime/time/source.rs
@@ -1,3 +1,4 @@
+use super::MAX_SAFE_MILLIS_DURATION;
 use crate::time::{Clock, Duration, Instant};
 
 /// A structure which handles conversion from Instants to u64 timestamps.
@@ -25,7 +26,7 @@ impl TimeSource {
             .unwrap_or_else(|| Duration::from_secs(0));
         let ms = dur.as_millis();
 
-        ms.try_into().unwrap_or(u64::MAX)
+        ms.try_into().unwrap_or(MAX_SAFE_MILLIS_DURATION)
     }
 
     pub(crate) fn tick_to_duration(&self, t: u64) -> Duration {
diff --git a/tokio/tests/time_sleep.rs b/tokio/tests/time_sleep.rs
index 4174a73b1f6..94022e3c00c 100644
--- a/tokio/tests/time_sleep.rs
+++ b/tokio/tests/time_sleep.rs
@@ -267,6 +267,20 @@ async fn exactly_max() {
     time::sleep(ms(MAX_DURATION)).await;
 }
 
+#[tokio::test]
+async fn issue_5183() {
+    time::pause();
+
+    let big = std::time::Duration::from_secs(u64::MAX / 10);
+    // This is a workaround since awaiting sleep(big) will never finish.
+    #[rustfmt::skip]
+    tokio::select! {
+	biased;
+        _ = tokio::time::sleep(big) => {}
+        _ = tokio::time::sleep(std::time::Duration::from_nanos(1)) => {}
+    }
+}
+
 #[tokio::test]
 async fn no_out_of_bounds_close_to_max() {
     time::pause();