Here are my suggestions:
Step 1: simply copy the graph.db folder.
Step 2: Go to 4.3 or any higher version
Step 3: Paste the folder from Step 2 in data/databases folder of Step 2.
Step 4: Open the terminal (from Step 3) and run this:
bin/neo4j-admin copy --from-database=graph.db --to-database=graphdb --force
(select any name for to-database)
Step 5: Once step 5 is successful, then run in Terminal:
bin/neo4j-admin store-info data/databases/graphdb (replace graphdb with the correct name)
Result should show:Store format version: SF4.3.0
Store format introduced in: 4.3.0
Once all the above steps are completed, copy the graphdb folder from data/databases (as in Step 5).
Step 6: Paste the copied db folder in V5.5 or above data/databases folder.
Final Step: Open Terminal and run this: bin/neo4j-admin database copy graphdb graphdb5 --force
Final Check: In Terminal run this:bin/neo4j-admin database info graphdb5 (use the correct name)
Result should show you format version 5 info.
That's all!
Check this link: