I have an ASA 5550 firewall that doesn't support TLS 1.2.
What impact would we have when the older protocols are disabled? Will this affect the servers at all?
The link provided by Schroeder is your answer to this one.
As a side note, looking at the data sheet for your ASA I would heavily recommend moving over to something new(er) - they stopped selling those back in 2013 and they lose support Sep-2018 in this case rather than just constantly upgrading all the time to get the latest features my best advice would be, replace that device.
Once Cisco stops supporting it (Sep-2018) you're going to have an incredibly hard time with getting support if something goes wrong, etc and that is a place you don't want to be (From experience) it's better to just upgrade entirely in this scenario.