Can not post in laravel 5 over jquery Ajax

@Chris's comment is correct :)

You simply need to remove the / from the end of your url. Your ajax request should go to http://domain.com/backend/get_subdirectories.

The reason is, because within the public/.htaccess file it will 301 redirect all urls with a trailing slash to the same url without one. The code that does it is here:

# Redirect Trailing Slashes If Not A Folder...RewriteCond %{REQUEST_FILENAME} !-dRewriteRule ^(.*)/$ /$1 [L,R=301]

Now the real issue is, the client will preform a GET request to the URL specified by the 301 redirect.

Wait! Why would it do this???

Well, we can look to RFC7231 for the answer. It says

6.4.2. 301 Moved Permanently

The 301 (Moved Permanently) status code indicates that the target
resource has been assigned a new permanent URI and any future
references to this resource ought to use one of the enclosed URIs.
Clients with link-editing capabilities ought to automatically re-linkreferences to the effective request URI to one or more of the new
references sent by the server, where possible.

The server SHOULD generate a Location header field in the responsecontaining a preferred URI reference for the new permanent URI. The
user agent MAY use the Location field value for automatic
redirection. The server's response payload usually contains a short
hypertext note with a hyperlink to the new URI(s).

  Note: For historical reasons, a user agent MAY change the request  method from POST to GET for the subsequent request.  If this  behavior is undesired, the 307 (Temporary Redirect) status code  can be used instead.

A 301 response is cacheable by default; i.e., unless otherwise
indicated by the method definition or explicit cache controls (see
Section 4.2.2 of [RFC7234]).

Now what's interesting is the note at the bottom that specifies that the user agent MAY change the request method from POST to GET. And it seems most user agents from browsers to frameworks, seem to follow that rule.