According to this documentation it should be possible to enable an SSH connection to a Cisco ASA 5505. However, it is not possible to ping an IP from the ASA while this has been configured. As it is impossible to ping internally then SSH from another system will work neither.
ciscoasa# sh run ... interface Vlan 100 nameif inside security-level 100 ip address 192.168.0.10 255.255.255.0 !
Ping from ASA
ciscoasa# ping 192.168.0.10 Type escape sequence to abort. Sending 5, 100-byte ICMP Echos to 192.168.0.10, timeout is 2 seconds: No route to host 192.168.0.10 Success rate is 0 percent (0/1)