*.core files are usually generated by the linux OS when an un handled exception crashes an application, and it include (hopefully) useful deugging information that can help you analyze the cause. From the name of the file it was probably generated from a php5fcgi.
But…. those files for sure should not be in your wordpress directory, so first go ahead and remove them from there. You should try to inspect one of them and make sure it is total gibrish and nothing that seems like any software code. Assuming it is not malicious, you should keep monitoring for their appearance, and if they do appear again, you should definitely look how to prevent them from appearing in the wordpress directories as they might include sensitive information.
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