diff --git a/guava-tests/test/com/google/common/io/FileBackedOutputStreamTest.java b/guava-tests/test/com/google/common/io/FileBackedOutputStreamTest.java
index 3cbf5a1028a7..ee7b43059187 100644
--- a/guava-tests/test/com/google/common/io/FileBackedOutputStreamTest.java
+++ b/guava-tests/test/com/google/common/io/FileBackedOutputStreamTest.java
@@ -171,4 +171,90 @@ private static boolean isAndroid() {
   private static boolean isWindows() {
     return OS_NAME.value().startsWith("Windows");
   }
+
+  /**
+   * Test that verifies the resource leak fix for Issue #5756.
+   *
+   * This test covers a scenario where we write a smaller amount of data first,
+   * then write a large amount that crosses the threshold (transitioning from
+   * "not at threshold" to "over the threshold"). This differs from the existing
+   * testThreshold() which writes exactly enough bytes to fill the buffer, then
+   * immediately writes more bytes.
+   *
+   * Note: Direct testing of the IOException scenario during write/flush is challenging
+   * without mocking. This test verifies that normal operation with threshold crossing
+   * still works correctly with the fix in place.
+   */
+  public void testThresholdCrossing_ResourceManagement() throws Exception {
+    // Test data that will cross the threshold
+    int threshold = 50;
+    byte[] beforeThreshold = newPreFilledByteArray(40);
+    byte[] afterThreshold = newPreFilledByteArray(30);
+
+    FileBackedOutputStream out = new FileBackedOutputStream(threshold);
+    ByteSource source = out.asByteSource();
+
+    // Write data that doesn't cross threshold
+    out.write(beforeThreshold);
+    assertNull(out.getFile());
+
+    // Write data that crosses threshold - this exercises the fixed code path
+    if (!JAVA_IO_TMPDIR.value().equals("/sdcard")) {
+      out.write(afterThreshold);
+      File file = out.getFile();
+      assertNotNull(file);
+      assertTrue(file.exists());
+
+      // Verify all data was written correctly
+      byte[] expected = new byte[70];
+      System.arraycopy(beforeThreshold, 0, expected, 0, 40);
+      System.arraycopy(afterThreshold, 0, expected, 40, 30);
+      assertTrue(Arrays.equals(expected, source.read()));
+
+      // Clean up
+      out.close();
+      out.reset();
+      assertFalse(file.exists());
+    }
+  }
+
+  /**
+   * Test that verifies writes after crossing the threshold work correctly.
+   *
+   * Once the threshold is crossed, subsequent writes go to the file. This test
+   * ensures that continued writing after the initial threshold crossing works
+   * properly with the resource management fix in place.
+   */
+  public void testWriteAfterThresholdCrossing() throws Exception {
+    // Use a small threshold to force multiple file operations
+    int threshold = 10;
+    FileBackedOutputStream out = new FileBackedOutputStream(threshold);
+    ByteSource source = out.asByteSource();
+
+    // Write data in chunks: first below threshold, then crossing it, then after crossing
+    byte[] chunk1 = newPreFilledByteArray(8);  // Below threshold
+    byte[] chunk2 = newPreFilledByteArray(5);  // Crosses threshold
+    byte[] chunk3 = newPreFilledByteArray(20); // More data to file
+
+    out.write(chunk1);
+    assertNull(out.getFile());
+
+    if (!JAVA_IO_TMPDIR.value().equals("/sdcard")) {
+      out.write(chunk2);
+      File file = out.getFile();
+      assertNotNull(file);
+
+      out.write(chunk3);
+
+      // Verify all data is correct
+      byte[] expected = new byte[33];
+      System.arraycopy(chunk1, 0, expected, 0, 8);
+      System.arraycopy(chunk2, 0, expected, 8, 5);
+      System.arraycopy(chunk3, 0, expected, 13, 20);
+      assertTrue(Arrays.equals(expected, source.read()));
+
+      out.close();
+      out.reset();
+    }
+  }
 }
diff --git a/guava/src/com/google/common/io/FileBackedOutputStream.java b/guava/src/com/google/common/io/FileBackedOutputStream.java
index ee7cc83c5d1d..4fe78aac11cd 100644
--- a/guava/src/com/google/common/io/FileBackedOutputStream.java
+++ b/guava/src/com/google/common/io/FileBackedOutputStream.java
@@ -238,13 +238,22 @@ private void update(int len) throws IOException {
         // this is insurance.
         temp.deleteOnExit();
       }
+      // Create and populate the file, ensuring proper resource management
+      FileOutputStream transfer = null;
       try {
-        FileOutputStream transfer = new FileOutputStream(temp);
+        transfer = new FileOutputStream(temp);
         transfer.write(memory.getBuffer(), 0, memory.getCount());
         transfer.flush();
         // We've successfully transferred the data; switch to writing to file
         out = transfer;
       } catch (IOException e) {
+        if (transfer != null) {
+          try {
+            transfer.close();
+          } catch (IOException closeException) {
+            e.addSuppressed(closeException);
+          }
+        }
         temp.delete();
         throw e;
       }