BuddyPress.org

You will need to supply more information than you have, i.e versions installed, although I asume they are latest stable releases of both.

This is not a common error; WP and BP normally install just fine, 500 is a server error and can be caused by a mis-configured .htaccess rule or lack of PHP script memory and many other factors.

Can you initially confirm how much memory is allocated to PHP script limit it may need to be increased, also what version of PHP you have installed on the server.

Does WP run ok? Don’t activate BP just ensure that WP is installed correctly, that permalinks work as expected.

If you can’t access dashboard rename BP plugin to force a deactivation of it and that should return access to wp-admin