diff --git a/libcontainer/specconv/spec_linux.go b/libcontainer/specconv/spec_linux.go
index 957011b4519..162195d8e4e 100644
--- a/libcontainer/specconv/spec_linux.go
+++ b/libcontainer/specconv/spec_linux.go
@@ -1164,11 +1164,11 @@ func parseMountOptions(options []string) *configs.Mount {
 			} else {
 				recAttrSet |= f.flag
 				recAttrClr &= ^f.flag
-				if f.flag&unix.MOUNT_ATTR__ATIME == f.flag {
-					// https://man7.org/linux/man-pages/man2/mount_setattr.2.html
-					// "cannot simply specify the access-time setting in attr_set, but must also include MOUNT_ATTR__ATIME in the attr_clr field."
-					recAttrClr |= unix.MOUNT_ATTR__ATIME
-				}
+			}
+			if f.flag&unix.MOUNT_ATTR__ATIME == f.flag {
+				// https://man7.org/linux/man-pages/man2/mount_setattr.2.html
+				// "cannot simply specify the access-time setting in attr_set, but must also include MOUNT_ATTR__ATIME in the attr_clr field."
+				recAttrClr |= unix.MOUNT_ATTR__ATIME
 			}
 		} else if f, exists := extensionFlags[o]; exists {
 			if f.clear {
diff --git a/tests/integration/mounts_recursive.bats b/tests/integration/mounts_recursive.bats
index b3ce579fc02..fdb9daba901 100644
--- a/tests/integration/mounts_recursive.bats
+++ b/tests/integration/mounts_recursive.bats
@@ -23,7 +23,7 @@ function teardown_volume() {
 
 function setup() {
 	setup_volume
-	setup_busybox
+	setup_debian
 }
 
 function teardown() {
@@ -76,3 +76,53 @@ function teardown() {
 	[ "$status" -eq 1 ]
 	[[ "${output}" == *"Read-only file system"* ]]
 }
+
+# https://github.com/opencontainers/runc/issues/5095
+@test "runc run [ check rbind,r*atime mounts]" {
+	requires_kernel 5.12
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt1\", options: [\"rbind\",\"ratime\"]}]"
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt2\", options: [\"rbind\",\"rnoatime\"]}]"
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt3\", options: [\"rbind\",\"rstrictatime\"]}]"
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt4\", options: [\"rbind\",\"rnostrictatime\"]}]"
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt5\", options: [\"rbind\",\"rrelatime\"]}]"
+	update_config ".mounts += [{source: \"${TESTVOLUME}\" , destination: \"/mnt6\", options: [\"rbind\",\"rnorelatime\"]}]"
+
+	runc run -d --console-socket "$CONSOLE_SOCKET" test_rbind_ratime
+	[ "$status" -eq 0 ]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt1
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt1/subvol
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt2
+	[[ "${output}" == "rw,noatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt2/subvol
+	[[ "${output}" == "rw,noatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt3
+	[[ "${output}" == "rw,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt3/subvol
+	[[ "${output}" == "rw,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt4
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt4/subvol
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt5
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt5/subvol
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt6
+	[[ "${output}" == "rw,relatime,"* ]]
+
+	runc exec test_rbind_ratime findmnt --noheadings -o options /mnt6/subvol
+	[[ "${output}" == "rw,relatime,"* ]]
+}