After much tracking things down in this forum and elsewhere, I now have six subsites functioning reasonably well under a mainsite hosted by Site5. I also have a single subsite under another mainsite hosted by Site5. Everything works as it should, except as noted below. In all cases, the subsites point to the root of the main site which is where Drupal is installed. Thus, they point to www.mainsite.com.
There is only one problem: whenever someone performs an operation to administer the site or calls for a wrong page, the browser "transfers" (that is what actually shows in a viewing window, "transferring") to the home page of the mainsite with an "access denied" message. By using the browser's back button, you can go back to the page in the subsite and pickup where you left off. This is a correctable annoyance for someone like myself who likes tinkering with things to make them just right. It would not be acceptable for the general audience.
I had thought this might be a "rewrite" issue. However, trying all the rewrite suggestions that might seem to apply, I can say from experience that none of them really work.
Once I solve this problem, everything will be quite satisfactory, particularly, since Site5 givens unlimited domain pointers which is the starting point for the approach I used.
Does anyone haev any suggestons? I am particulalry interested in hearing about how others tackled the multisite problem on Site5.