This slight modification clears all contents of the to be pasted sheet before doing the copy paste
Sub Button1_Click()
Dim ws As Worksheet, ds As Worksheet
Dim lRow As Long
Set ws = ThisWorkbook.Worksheets("Source")
Set ds = ThisWorkbook.Worksheets("Reconcile")
ds.Range(ds.Cells(5, 1), ds.Cells(ds.UsedRange.Rows.Count, ds.UsedRange.Columns.Count)).Clear
lRow = ws.Range("C65536").End(xlUp).Row
ws.Range("C5:C" & lRow).Copy ds.Range("A5")
ws.Range("H6:H" & lRow).Copy ds.Range("C5")
ws.Range("J6:J" & lRow).Copy ds.Range("E5")
End Sub