Index: Python/pystrtod.c
===================================================================
--- Python/pystrtod.c	(revision 72259)
+++ Python/pystrtod.c	(working copy)
@@ -755,7 +755,7 @@
 			PyErr_BadInternalCall();
 			return NULL;
 		}
-		precision = 12;
+		precision = PyFloat_STR_PRECISION;
 		format_code = 'g';
 		break;
 	default:
@@ -1228,7 +1228,7 @@
 			PyErr_BadInternalCall();
 			return NULL;
 		}
-		precision = 12;
+		precision = PyFloat_STR_PRECISION;
 		break;
 
 	default:
Index: Include/floatobject.h
===================================================================
--- Include/floatobject.h	(revision 72258)
+++ Include/floatobject.h	(working copy)
@@ -21,6 +21,8 @@
 #define PyFloat_Check(op) PyObject_TypeCheck(op, &PyFloat_Type)
 #define PyFloat_CheckExact(op) (Py_TYPE(op) == &PyFloat_Type)
 
+#define PyFloat_STR_PRECISION 12
+
 #ifdef Py_NAN
 #define Py_RETURN_NAN return PyFloat_FromDouble(Py_NAN)
 #endif
Index: Objects/stringlib/formatter.h
===================================================================
--- Objects/stringlib/formatter.h	(revision 72258)
+++ Objects/stringlib/formatter.h	(working copy)
@@ -881,6 +881,7 @@
     int has_decimal;
     double val;
     Py_ssize_t precision = format->precision;
+    Py_ssize_t default_precision = 6;
     STRINGLIB_CHAR type = format->type;
     int add_pct = 0;
     STRINGLIB_CHAR *p;
@@ -910,6 +911,7 @@
         /* Omitted type specifier. This is like 'g' but with at least
            one digit after the decimal point. */
         type = 'g';
+        default_precision = PyFloat_STR_PRECISION;
         flags |= Py_DTSF_ADD_DOT_0;
     }
 
@@ -933,7 +935,7 @@
     }
 
     if (precision < 0)
-        precision = 6;
+        precision = default_precision;
 
 #if PY_VERSION_HEX < 0x03010000
     /* 3.1 no longer converts large 'f' to 'g'. */
@@ -1039,6 +1041,7 @@
     int re_has_decimal;
     int im_has_decimal;
     Py_ssize_t precision = format->precision;
+    Py_ssize_t default_precision = 6;
     STRINGLIB_CHAR type = format->type;
     STRINGLIB_CHAR *p_re;
     STRINGLIB_CHAR *p_im;
@@ -1100,6 +1103,7 @@
     if (type == '\0') {
         /* Omitted type specifier. Should be like str(self). */
         type = 'g';
+        default_precision = PyFloat_STR_PRECISION;
         add_parens = 1;
         if (re == 0.0)
             skip_re = 1;
@@ -1115,7 +1119,7 @@
         type = 'f';
 
     if (precision < 0)
-        precision = 6;
+        precision = default_precision;
 
     /* Cast "type", because if we're in unicode we need to pass a
        8-bit char. This is safe, because we've restricted what "type"
Index: Lib/test/test_complex.py
===================================================================
--- Lib/test/test_complex.py	(revision 72258)
+++ Lib/test/test_complex.py	(working copy)
@@ -445,6 +445,16 @@
         self.assertEqual(format(3+0j, ''), str(3+0j))
         self.assertEqual(format(3.2+0j, ''), str(3.2+0j))
 
+        # empty presentation type should still be analogous to str,
+        # even when format string is nonempty (issue #5920).
+        self.assertEqual(format(3.2+0j, '-'), str(3.2+0j))
+        self.assertEqual(format(3.2+0j, '<'), str(3.2+0j))
+        z = 4/7. - 100j/7.
+        self.assertEqual(format(z, ''), str(z))
+        self.assertEqual(format(z, '-'), str(z))
+        self.assertEqual(format(z, '<'), str(z))
+        self.assertEqual(format(z, '10'), str(z))
+
         self.assertEqual(format(1+3j, 'g'), '1+3j')
         self.assertEqual(format(3j, 'g'), '0+3j')
         self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j')
Index: Lib/test/test_float.py
===================================================================
--- Lib/test/test_float.py	(revision 72258)
+++ Lib/test/test_float.py	(working copy)
@@ -284,6 +284,13 @@
         self.assertEqual(format(0.01, ''), '0.01')
         self.assertEqual(format(0.01, 'g'), '0.01')
 
+        # empty presentation type should format in the same way as str
+        # (issue 5920)
+        x = 100/7.
+        self.assertEqual(format(x, ''), str(x))
+        self.assertEqual(format(x, '-'), str(x))
+        self.assertEqual(format(x, '>'), str(x))
+        self.assertEqual(format(x, '2'), str(x))
 
         self.assertEqual(format(1.0, 'f'), '1.000000')