If you have an existing account or "entitlement" from a past purchase, you can try searching the Broadcom Support Portal. However, older versions are frequently hidden or restricted to those with active support contracts.
Finding a legitimate is increasingly difficult following the Broadcom acquisition of VMware. Since ESXi 5.5 is more than a decade old and officially unsupported, it has been removed from most public-facing general download pages. Where to Find VMware ESXi 5.5 ISO Downloads vmware esxi 5.5 iso download
After installation, use the Direct Console User Interface (DCUI) to set a static IP address and hostname. Should You Still Use ESXi 5.5? If you have an existing account or "entitlement"
Once you have secured the ISO, the installation process generally follows these steps: Since ESXi 5
Major hardware vendors like Dell , HP , and Lenovo often host customized ESXi 5.5 images designed for their specific server hardware. These are typically the easiest "official" versions to find.
Use a tool like Rufus or Etcher to burn the ISO to a USB flash drive or CD.
Install VMware ESXi & Create Your First VM: Step-by-Step - StarWind