Even without a contract, your ASA 5505 stores ASDM images locally. Use a browser that still supports Java (e.g., Internet Explorer 11 or an older Firefox portable build):
The ASA must be configured to allow HTTPS management access. Step-by-Step Download & Installation Enable HTTPS on the ASA: cisco asa 5505 asdm-idm launcher download
The launcher requires Java to run. For older ASA 5505 setups, Oracle JRE 7.45 is often recommended for better compatibility. Management IP: Even without a contract, your ASA 5505 stores