Need to come up with a bash script that will add text to new line in a file.
eg: File "append"
line1
line2
line3

Need to come up with a script that will add line 4 and line 5 after line3 as follows to append file:
line1
line2
line3
line4
line5

I hope I have understood your question correctly -
If you have a file called append.txt containing

line1
line2
line3

If you need to add line4 and line5 below line3, all that is needed is to append
to this already existing append.txt file
Can be done by giving in the script -

echo "line4" >> append.txt
echo "line5" >> append.txt

Let me know if what I understood was not your question