diff --git a/M/Manopt/Compat.toml b/M/Manopt/Compat.toml
index 511afa341841ef1..9b1b02397f3ffa8 100644
--- a/M/Manopt/Compat.toml
+++ b/M/Manopt/Compat.toml
@@ -87,12 +87,12 @@ StaticArrays = "0.12"
 ["0.2.7-0.2.10"]
 Manifolds = "0.4.1-0.4"
 
-["0.3-0"]
-Requires = ["0.5", "1"]
-
 ["0.3-0.3.5"]
 ManifoldsBase = "0.10.3-0.10"
 
+["0.3-0.5.4"]
+Requires = ["0.5", "1"]
+
 ["0.3.10-0.3.11"]
 ManifoldsBase = "0.11-0.12"
 
@@ -146,7 +146,13 @@ ManifoldsBase = "0.14.10-0.14"
 ["0.4.40-0.4.56"]
 ManifoldsBase = "0.15"
 
-["0.4.41-0"]
+["0.4.41-0.4.60"]
+Test = "1.6.0-1"
+
+["0.4.41-0.5.3"]
+ManifoldDiff = "0.3.8-0.3"
+
+["0.4.41-0.5.4"]
 Dates = "1.6.0-1"
 LinearAlgebra = "1.6.0-1"
 Markdown = "1.6.0-1"
@@ -154,12 +160,6 @@ Printf = "1.6.0-1"
 Random = "1.6.0-1"
 SparseArrays = "1.6.0-1"
 
-["0.4.41-0.4.60"]
-Test = "1.6.0-1"
-
-["0.4.41-0.5.3"]
-ManifoldDiff = "0.3.8-0.3"
-
 ["0.4.52-0"]
 Preferences = "1.4.0-1"
 
@@ -178,9 +178,6 @@ ManifoldsBase = "0.15.10-0.15"
 ["0.4.7"]
 ManifoldDiff = "0.2.1-0.3"
 
-["0.4.8-0"]
-Statistics = "1.6.0-1"
-
 ["0.4.8-0.4"]
 julia = "1.6.0-1"
 
@@ -190,7 +187,10 @@ ManifoldsBase = "0.13.30-0.14"
 ["0.4.8-0.4.22"]
 ManifoldDiff = "0.2-0.3"
 
-["0.5-0"]
+["0.4.8-0.5.4"]
+Statistics = "1.6.0-1"
+
+["0.5-0.5.4"]
 julia = "1.8.0-1"
 
 ["0.5.3-0"]
@@ -200,3 +200,13 @@ ManifoldsBase = "0.15.18-0.15"
 ColorTypes = "0.9.1-0.12"
 Colors = "0.11.2-0.13"
 ManifoldDiff = "0.3.8-0.4"
+
+["0.5.5-0"]
+Dates = "1.10.0-1"
+LinearAlgebra = "1.10.0-1"
+Markdown = "1.10.0-1"
+Printf = "1.10.0-1"
+Random = "1.10.0-1"
+SparseArrays = "1.10.0-1"
+Statistics = "1.10.0-1"
+julia = "1.10.0-1"
diff --git a/M/Manopt/Deps.toml b/M/Manopt/Deps.toml
index e52cf0d84269ff1..6d6d782d728dbff 100644
--- a/M/Manopt/Deps.toml
+++ b/M/Manopt/Deps.toml
@@ -43,7 +43,7 @@ DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 ["0.2.5-0.4.20"]
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
-["0.3-0"]
+["0.3-0.5.4"]
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 
 ["0.3.20-0"]
diff --git a/M/Manopt/Versions.toml b/M/Manopt/Versions.toml
index 2e811ac30dc735e..8c37c93f82da30d 100644
--- a/M/Manopt/Versions.toml
+++ b/M/Manopt/Versions.toml
@@ -435,3 +435,6 @@ git-tree-sha1 = "9800c519fde043f1ce6919df0a2e6cce014c13d1"
 
 ["0.5.4"]
 git-tree-sha1 = "8c9eeab575ab5b6d4466c0c9d20321e4d659b5ce"
+
+["0.5.5"]
+git-tree-sha1 = "98f097d46b6fc68ca3bef97942b3a9a3edbbd40d"