How can I move a 5 year old olive tree from one location in the garden to another?
The key points are to dig the root ball with as much soil as you can handle, and keep the soil intact around the roots with burlap wrapped in place with twine to hold it together, so the root ball doesn't break up and expose the roots to drying air. If it's heavy, get the help you need in order to avoid rough handling and breakage of the root ball. Move by lifting the soil root ball and not by lifting from the stem of the tree. Use a wheeled dolly and pickup lift gate if needed.
Have the new planting hole ready and make the move as swiftly and efficiently as you can, and get it watered in the new site as soon as possible. Don't let it sit and dry out. If you have a time lag between digging and planting, be sure to keep it in the shade and the burlap wrap moist so the root ball doesn't dry out.
Set the root ball in the new planting hole with the soil grade at the same level or slightly above the surrounding soil grade, not too low in the hole.
When you backfill the hole around the root ball, I prefer to water settle it, instead of tamping the soil firm. As you backfill, poke a running hose end down into the loose backfill to make sure the soil is settled with all the air pockets out.
Pick up some Superthirive and put a dash in the water as you backfill:
Here's an article with more tips: