diff --git a/backends-velox/src/test/scala/org/apache/gluten/execution/VeloxAggregateFunctionsSuite.scala b/backends-velox/src/test/scala/org/apache/gluten/execution/VeloxAggregateFunctionsSuite.scala
index df08174101f19..394c4e01651e8 100644
--- a/backends-velox/src/test/scala/org/apache/gluten/execution/VeloxAggregateFunctionsSuite.scala
+++ b/backends-velox/src/test/scala/org/apache/gluten/execution/VeloxAggregateFunctionsSuite.scala
@@ -371,8 +371,7 @@ abstract class VeloxAggregateFunctionsSuite extends VeloxWholeStageTransformerSu
     }
   }
 
-  // Disable for Spark3.5.
-  testWithSpecifiedSparkVersion("regr_r2", Some("3.3"), Some("3.4")) {
+  testWithSpecifiedSparkVersion("regr_r2", Some("3.3")) {
     runQueryAndCompare("""
                          |select regr_r2(l_partkey, l_suppkey) from lineitem;
                          |""".stripMargin) {
@@ -391,8 +390,7 @@ abstract class VeloxAggregateFunctionsSuite extends VeloxWholeStageTransformerSu
     }
   }
 
-  // Disable for Spark3.5.
-  testWithSpecifiedSparkVersion("regr_slope", Some("3.4"), Some("3.4")) {
+  testWithSpecifiedSparkVersion("regr_slope", Some("3.4")) {
     runQueryAndCompare("""
                          |select regr_slope(l_partkey, l_suppkey) from lineitem;
                          |""".stripMargin) {
@@ -411,8 +409,7 @@ abstract class VeloxAggregateFunctionsSuite extends VeloxWholeStageTransformerSu
     }
   }
 
-  // Disable for Sparke3.5.
-  testWithSpecifiedSparkVersion("regr_intercept", Some("3.4"), Some("3.4")) {
+  testWithSpecifiedSparkVersion("regr_intercept", Some("3.4")) {
     runQueryAndCompare("""
                          |select regr_intercept(l_partkey, l_suppkey) from lineitem;
                          |""".stripMargin) {
@@ -431,8 +428,7 @@ abstract class VeloxAggregateFunctionsSuite extends VeloxWholeStageTransformerSu
     }
   }
 
-  // Disable for Sparke3.5.
-  testWithSpecifiedSparkVersion("regr_sxy regr_sxx regr_syy", Some("3.4"), Some("3.4")) {
+  testWithSpecifiedSparkVersion("regr_sxy regr_sxx regr_syy", Some("3.4")) {
     runQueryAndCompare("""
                          |select regr_sxy(l_quantity, l_tax) from lineitem;
                          |""".stripMargin) {
diff --git a/gluten-iceberg/src/test/scala/org/apache/gluten/execution/VeloxTPCHIcebergSuite.scala b/gluten-iceberg/src/test/scala/org/apache/gluten/execution/VeloxTPCHIcebergSuite.scala
index f997693f82128..22a5b6b70be2c 100644
--- a/gluten-iceberg/src/test/scala/org/apache/gluten/execution/VeloxTPCHIcebergSuite.scala
+++ b/gluten-iceberg/src/test/scala/org/apache/gluten/execution/VeloxTPCHIcebergSuite.scala
@@ -17,14 +17,12 @@
 package org.apache.gluten.execution
 
 import org.apache.spark.SparkConf
+import org.apache.spark.sql.functions.col
 
 import org.apache.iceberg.spark.SparkWriteOptions
-import org.scalatest.Ignore
 
 import java.io.File
 
-// Ignored due to failures, see https://github.com/apache/incubator-gluten/issues/5362
-@Ignore
 class VeloxTPCHIcebergSuite extends VeloxTPCHSuite {
 
   protected val tpchBasePath: String = new File(
@@ -97,21 +95,21 @@ class VeloxTPCHIcebergSuite extends VeloxTPCHSuite {
   }
 }
 
-// Ignored due to failures, see https://github.com/apache/incubator-gluten/issues/5362
-@Ignore
 class VeloxPartitionedTableTPCHIcebergSuite extends VeloxTPCHIcebergSuite {
   override protected def createTPCHNotNullTables(): Unit = {
     TPCHTables.map {
       table =>
         val tablePath = new File(resourcePath, table.name).getAbsolutePath
-        val tableDF = spark.read.format(fileFormat).load(tablePath)
+        val tableDF = spark.read
+          .format(fileFormat)
+          .load(tablePath)
+          .repartition(table.partitionColumns.map(col): _*)
+          .sortWithinPartitions(table.partitionColumns.map(col): _*)
 
-        tableDF
-          .repartition(800)
-          .write
+        tableDF.write
           .format("iceberg")
           .partitionBy(table.partitionColumns: _*)
-          .option(SparkWriteOptions.FANOUT_ENABLED, "true")
+          .option(SparkWriteOptions.FANOUT_ENABLED, "false")
           .mode("overwrite")
           .saveAsTable(table.name)
         (table.name, tableDF)
diff --git a/shims/spark35/src/main/scala/org/apache/gluten/sql/shims/spark35/Spark35Shims.scala b/shims/spark35/src/main/scala/org/apache/gluten/sql/shims/spark35/Spark35Shims.scala
index 70e0b73ed3ac2..1e23b49f9a527 100644
--- a/shims/spark35/src/main/scala/org/apache/gluten/sql/shims/spark35/Spark35Shims.scala
+++ b/shims/spark35/src/main/scala/org/apache/gluten/sql/shims/spark35/Spark35Shims.scala
@@ -29,7 +29,7 @@ import org.apache.spark.sql.{AnalysisException, SparkSession}
 import org.apache.spark.sql.catalyst.{ExtendedAnalysisException, InternalRow}
 import org.apache.spark.sql.catalyst.catalog.BucketSpec
 import org.apache.spark.sql.catalyst.expressions._
-import org.apache.spark.sql.catalyst.expressions.aggregate.{BloomFilterAggregate, TypedImperativeAggregate}
+import org.apache.spark.sql.catalyst.expressions.aggregate.{BloomFilterAggregate, RegrIntercept, RegrR2, RegrReplacement, RegrSlope, RegrSXY, TypedImperativeAggregate}
 import org.apache.spark.sql.catalyst.plans.logical.LogicalPlan
 import org.apache.spark.sql.catalyst.plans.physical.{ClusteredDistribution, Distribution}
 import org.apache.spark.sql.catalyst.rules.Rule
@@ -71,7 +71,15 @@ class Spark35Shims extends SparkShims {
       Sig[Empty2Null](ExpressionNames.EMPTY2NULL))
   }
 
-  override def aggregateExpressionMappings: Seq[Sig] = Seq.empty
+  override def aggregateExpressionMappings: Seq[Sig] = {
+    Seq(
+      Sig[RegrR2](ExpressionNames.REGR_R2),
+      Sig[RegrSlope](ExpressionNames.REGR_SLOPE),
+      Sig[RegrIntercept](ExpressionNames.REGR_INTERCEPT),
+      Sig[RegrSXY](ExpressionNames.REGR_SXY),
+      Sig[RegrReplacement](ExpressionNames.REGR_REPLACEMENT)
+    )
+  }
 
   override def convertPartitionTransforms(
       partitions: Seq[Transform]): (Seq[String], Option[BucketSpec]) = {