I installed CiviCRM 1.5 with Drupal 5.0 following the same steps I took installing it with Drupal 4.7 and got no errors.
CiviCRM wouldn't show up in the modules list in the admin section, so I poked around a bit to see what the overall setup was of the Drupal 5.0 modules.
I moved the civicrm.css file into the main civicrm folder, moved the civicrm.module file into the main civicrm folder and then created a civicrm.info file and follwed the same format as the other .info files (a couple of lines of code describing the module) to write to the civicrm.info file. I copied the civicrm.settings.php file to drupal/sites/default folder and went back to the Drupal 5.0 admin area and lo and behold, CiviCRM 1.5 was there. I enabled it and it worked.
This is what worked for me using Control Panel, FTP, File Manager and PHPMyAdmin.
Before you begin make sure you have a working Drupal 4.7 already installed. Have the name of the database, database user and password handy as well as the name of your mysql host. If you can’t find the name of your mysql host anywhere on your host’s site then your mysql host is probably localhost. Save yourself the aggravation and get all these things written down beside you before you even start installing CiviCRM.
1. Use FTP to upload the zip/tar CiviCRM directly into the drupal/modules folder.
2. Go to your Control Panel or whatever method you use to create new databases and create a new database called civicrm. You will already have a database user name and password from your Drupal installation. Go to your list of database users and add a user to the new civicrm database you just created. Make sure to give the user full privileges.