Any faster version of the same code to handle 5000+ records

RE:Improving the algorithm will require some VBA skills, and some time to use those skills. Are you prepared to spend time to learn that? If yes, I can provide some guidance. 

option explicit
Sub RunMe_loaddata()

dim lC as long, lA as long
' lC is row number in sheet1, where the column of interest is C
' lA is row number in sheet2, where the column of interest is A

Sheets(1).Select

lC=2 
lA=2
do while not (isempty(Cells(lC,"C")) or isempty(Sheets(2).Cells(lA, "A"))) 
        If Cells(lC,"C").Value = Sheets(2).Cells(lA, "A").Value Then
                  Cells(lC,"C").EntireRow.Copy _
                      Sheets("Sheet4").Range("A" & Rows.Count).End(xlUp).Offset(1, 0)
                 Cells(lC,"C").Interior.Color = 65535
                 Sheets(2).Cells(lA, "A").Interior.Color = 65535
  ' assuming that values are unique, we can move to next rows in both sheets
                 lA=lA+1
                 lC=lC+1
       else
                 If Cells(lC,"C").Value < Sheets(2).Cells(x, "A").Value Then
                         lC=lC+1
                 else
                         lA=lA+1
                 end if
        End If
Loop 'while not (isempty(Cells(lC,"C")) or isempty(Sheets(2).Cells(x, "A")))

End Sub

Option Explicit

Sub CompareSolve()
Dim i As Long
Dim j As Long
Dim ar As Variant

 ar = Sheet2.Cells(1, 3).CurrentRegion.Value

    With CreateObject("Scripting.Dictionary")
     .CompareMode = 1
         For i = 2 To UBound(ar, 1)
            .Item(ar(i, 1)) = Empty
         Next

     ar = Sheet1.Cells(1).CurrentRegion.Value
     n = 1

        For i = 2 To UBound(ar, 1)
             If .exists(ar(i, 1)) Then
                 n = n + 1
            For j = 1 To UBound(ar, 2)
                 n = n + 1
                 ar(n, j) = ar(i, j)
             Next j
            End If
        Next i
    End With
Sheet3.Cells(1).Resize(n, UBound(ar, 2)).Value = ar
End Sub