diff --git a/package/MDAnalysis/core/topologyattrs.py b/package/MDAnalysis/core/topologyattrs.py
index 359bd20c9c..1285ebb2ac 100644
--- a/package/MDAnalysis/core/topologyattrs.py
+++ b/package/MDAnalysis/core/topologyattrs.py
@@ -2146,6 +2146,11 @@ class Charges(AtomAttr):
     transplants = defaultdict(list)
     dtype = float
 
+
+    def __init__(self, values, guessed=False, round_val=None):
+        super().__init__(values, guessed)
+        self.round = round_val
+
     @staticmethod
     def _gen_initial_values(na, nr, ns):
         return np.zeros(na)
@@ -2160,6 +2165,9 @@ def get_residues(self, rg):
             for i, row in enumerate(resatoms):
                 charges[i] = self.values[row].sum()
 
+        if self.round is not None:
+            charges = np.round(charges, self.round)
+
         return charges
 
     def get_segments(self, sg):
diff --git a/package/MDAnalysis/topology/TOPParser.py b/package/MDAnalysis/topology/TOPParser.py
index ba61bea0b0..603c8c70b5 100644
--- a/package/MDAnalysis/topology/TOPParser.py
+++ b/package/MDAnalysis/topology/TOPParser.py
@@ -453,7 +453,12 @@ def parse_charges(self, num_per_record, numlines):
         vals = self.parsesection_mapper(numlines, lambda x: float(x))
         charges = np.array(vals, dtype=np.float32)
         charges /= 18.2223  # to electron charge units
-        attr = Charges(charges)
+        # in practice, the precision of partial charges
+        # in MD simulation forcefields is typically limited
+        # to a few decimal places (i.e., 1e-4 is already optimistic)
+        # see gh-5032
+        # here, we round the residue net charges to 4 decimal places
+        attr = Charges(charges, round_val=4)
         return attr
 
     def parse_masses(self, num_per_record, numlines):
diff --git a/testsuite/MDAnalysisTests/topology/test_top.py b/testsuite/MDAnalysisTests/topology/test_top.py
index a67c9283b7..5e2a92dc41 100644
--- a/testsuite/MDAnalysisTests/topology/test_top.py
+++ b/testsuite/MDAnalysisTests/topology/test_top.py
@@ -27,7 +27,7 @@
 import MDAnalysis as mda
 import numpy as np
 import pytest
-from numpy.testing import assert_equal
+from numpy.testing import assert_equal, assert_allclose
 
 from MDAnalysisTests.datafiles import PRM  # ache.prmtop
 from MDAnalysisTests.datafiles import PRM7  # tz2.truncoct.parm7.bz2
@@ -837,3 +837,29 @@ def test_warning(self, parm, errmsgs):
 
         for msg in errmsgs:
             assert any(msg in recmsg for recmsg in messages)
+
+
+def test_gh_5032():
+    u = mda.Universe(PRM)
+    # check individual residue.charge
+    actual = []
+    for res in u.residues:
+        actual.append(res.charge)
+    expected = [1.0, # N-terminal A
+                -1.0, # E
+                0.0, # F
+                0.0, # H (HIE)
+                1.0, # R
+                0.0, # W
+                0.0, # S
+                0.0, # S
+                0.0, # Y
+                0.0, # M
+                0.0, # V
+                0.0, # H (HIE)
+                0.0, # W
+                0.0] # C-terminal K
+    assert_allclose(actual, expected)
+    # check residues.charges, which are set
+    # separately
+    assert_allclose(u.residues.charges, expected)