Hi Ivan,
From the security perspective is higly recommeded to have the network devices using the most secure protocols available, as you mention unfortunately the ASA5505 does not support TLS1.2 due to the hardware limitation.
Implement a BEAST attack is extremely complex and have a low chance of sucess, however there is always the possibilit that someone can exploit this vulnerabiliy.
I found the following forum intersting, I hope it clears your doubts about BEAST and TLSv1.0 vulnerabilities.
https://community.qualys.com/blogs/securitylabs/2013/09/10/is-beast-still-a-threat
Hope it helps.
-Randy-