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
It turns out that it was running 32M or memory, so I created a .htaccess that increased that to 64M
Now the WP works, but the database is generating errors that the table it is looking for doesnt exist.
Here is the error from the log. Note, I am hosting this in Rackspace Cloud (CloudSites):
[22-Sep-2010 09:15:23] WordPress database error Table ***********.wp_bp_xprofile_groups’ doesn’t exist for query SELECT id FROM wp_bp_xprofile_groups WHERE id = 1 made by require_once, require, do_action, call_user_func_array, xprofile_add_admin_menu, xprofile_install
[22-Sep-2010 09:15:23] WordPress database error Table ***********.wp_bp_xprofile_fields’ doesn’t exist for query SELECT id FROM wp_bp_xprofile_fields WHERE id = 1 made by require_once, require, do_action, call_user_func_array, xprofile_add_admin_menu, xprofile_install
Note, I replaced my DB name with ***********
I would check all settings in the BP admin section, possibly deactivate/reactivate BP.
Are you running anything other than a bog standard install?
Check the DB do these tables exist?
What’s probably happened is that the site out-of-memory’d during the initial installation, so you may need to clean your database and re-install BuddyPress.
I host on RackSpace (Cloud Sites) this normally isn’t a problem ever. Do what Paul Gibbs suggests above and then increase the memory allocated for PHP by editing the wp-config.php: https://codex.wordpress.org/Editing_wp-config.php#Increasing_memory_allocated_to_PHP
