Try making your table into a proper Excel Table (with no blank rows at the bottom) and instead of the chart data range being the likes of =Sheet1!$A$5:$C$23 it will start off looking like, say, =Table1. Now when you add data below the bottom of the table, the table will (should) expand to include the new data, and so will the chart.
If you go back into Select Data… you may well find the old range address style =Sheet1!$A$5:$C$23 is still there, but it should still follow the size of the table.
If ever you want to change what's plotted, you can manually change the size of the table by dragging the table's grab-handle at bottom right of the table.