Busy signal detection

Does Asterisk support busy signal detection over SIP?

Calls come in through the PSTN to a Cisco 5350 then over SIP to Asterisk.

do you mean, if a call comes into an extension that is busy? If so then yes it will play the voicemail greeting or play a busy tone if you do not have another call path, for example, my grandstream gxp2000 phones have 4 call appearances and if I am on a call my 2nd one will ring. So it has some to do with asterisk and some to do with the phones

I mean if Asterisk originates a call through the Cisco 5350 to the PSTN and the number dialed is busy - can this be detected ?

I don’t believe asterisk will do call-progress detection on an RTP stream, i could be wrong.

Generally that is the responsibility of the PSTN gateway device. The inband busy signal is generally converted to a SIP 400 series error.