What you want to achieve is an insert edit.
Select the clips on the timeline
Hit CTRL/CMD+C (if you want the original clips to stay where they are) or
CTRL/CMD+X (if you want to move the clips)
Next, place the cursor between part 1 and part 2.
(You may need to activate S on your keyboard to activate Snap in timeline, so that your cursor will snap between clips)
Hit CTRL/CMD+SHIFT+V to do an Insert Edit, effectively pasting the clips from memory (part 5) between part 1 and 2.
The alternative method is to drag enough space between part 1 and 2 (select all clips from part 2 upto the end of the sequence and drag them to the right), so as to accomodate for part 5. Then, select clips from part 5 and align to the end of part 1. Next, select all other clips, right of - now - part 5 and drag them to close the gap. You may also use the Ripple delete function found under your right-click menu.
Hope this helps.