Did you ever find a solution to this problem? I'm running into the same issue with Laravel 5 and XAMPP (with PHP 5.5).

I've setup OpenSSL properly as stated in many different sources (including the .dll copying and multiple INI uncomments), but still I'm running into this "OpenSSL required" error.

I've setup an Apache virtual host block that routes traffic from localdomain.dev:80 to the Laravel public directory. Would some Apache virtual host configuration set this off (though Javacadabra's problem is reproduced with non-domain installation)?

Also about the times that the application loads fine right after a reboot: could Laravel or Apache or PHP set some system cache data that could break the setup after a single page load?

(Yes, I could just boot up Homestead or a Linux VM to do my work. Instead I want a solution to this nagging problem.)

EDIT: Found a solution. Apache's OpenSSL related binaries need to be probably updated manually in C:\xampp\apache\bin. Download the standalone package ZIP from this listing (I picked 1.0.2 x64) and extract the files to said folder. Worked for me at least.