Our research reveals two significant vulnerabilities in Microsoft Azure Private 5G Core (AP5GC). The first vulnerability (CVE-2024-20685) allows a crafted signaling message to crash the control plane, leading to potential service outages. The second (ZDI-CAN-23960) disconnects and replaces attached base stations, disrupting network operations. While these issues are implementation-specific, their exploitation is made possible by a systemic weakness: the lack of mandatory authentication procedures between base stations and packet-cores.