The short answer is run the version 11 dbunload.exe utility on your version 5.5 database file.

The following Windows command script shows how to upgrade the version 5.5 sademo.db into a brand-new ddd11.db file.

There is often a lot more to upgrading across 6 major releases, but this is a starting point...

REM If you're a command-line kinda guy, here is my template Windows 
REM batch file run_dbunload_upgrade_v5_to_v11.bat. It does the 
REM unload-reload-all-in-one-dbunload-step, then starts dbeng11 
REM and dbisql so you can make sure the new database is up and running.

REM Be sure to stop *all* database engines on the computer you're using, 
REM before starting the upgrade.

REM dbunload...
REM -an ...  where to put new database
REM -ap ...  new database page size
REM -c ...   old database startup connection string
REM -o ...   where to put unload console display text file
REM -v       verbose mode for console display

PAUSE MAKE SURE YOU DO NOT HAVE ANY ENGINES RUNNING.

"%SQLANY11%\bin32\dbunload.exe"^
  -an ddd11.db^
  -ap 4096^
  -c "DBF=sademo.db;UID=dba;PWD=sql"^
  -o dbunload_log_sademo.txt^
  -v

PAUSE dbunload/reload done...

REM dbeng11...
REM -c ...    initial RAM cache size
REM -o ...    where to put server console display text file
REM -os ...   when to rename and restart server console display text file
REM ddd11.db  new database to start

"%SQLANY11%\bin32\dbspawn.exe"^
  -f "%SQLANY11%\bin32\dbeng11.exe"^
  -o dbeng11_log_ddd11.txt^
  ddd11.db

PAUSE dbeng11 started...

REM dbisql...
REM -c ...   new database connection string

"%SQLANY11%\bin32\dbisql.exe"^
  -c "ENG=ddd11;DBN=ddd11;UID=dba;PWD=sql"

PAUSE dbisql running...