-vv gave a response, I presume the issue is authentication related.
curl-apd -vv -g -s --ntlm -k -X POST -H 'Content-Type: text/xml; charset=utf-8' -d "<?xml version="1.0" encoding="UTF-8"?><soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/" xmlns:t="http://schemas.microsoft.com/exchange/services/2006/types" xmlns:m="http://schemas.microsoft.com/exchange/services/2006/messages"><soap:Header></soap:Header><soap:Body><GetFolderxmlns="http://schemas.microsoft.com/exchange/services/2006/messages"><t:BaseShape>IdOnly</t:BaseShape><t:DistinguishedFolderId Id="inbox"><t:Mailbox><t:EmailAddress>F5HealthCheck1@webdomain.com</t:EmailAddress></t:Mailbox></t:DistinguishedFolderId></soap:Body></soap:Envelope>" -u 'AD_DOMAIN.com\saf5healthcheck1':******** http://10.130.172.31:443/EWS/Exchange.asmx | grep -i "<m:GetFolderResponseMessage ResponseClass="Success">"
Thanks so much for your assistance! I feel like this is enough to keep pursuing with the Exchange admin.