Export the contacts out of the Verizon Cloud to vCard file and import them into your Google account. Use a computer for this task.
Then you can sign into your Google account on the LG Nexus 5x and wait for the contacts to sync with the phone.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
We can clarify. On Basic Device you may see Verizon Cloud listed instead as Backup Assistant. KleoL_VZW
Follow us on Twitter @VZWSupport
If my response answered your question please click the "Correct Answer" button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!