Yes you can FTP from inside HomeSite 5.5. You need to set up a 'Deployment Server' inside your project. Search for FTP or Deployment Server inside HomeSite's help files for full information.
Also if you double-click 'My Computer' under 'Other' you should see 'Macromedia FTP & RDS'. You can set up Deployment Servers from there.
Here's some links to support pages that might also help:
They were written for v4.5 but nothing much has changed in v5.5 except for the addition of being able to upload individual files and folders instead of entire projects.
This site has a lot more HS tips that you might find useful: