i can receive but not send e-mails through mac mail app i can use g-mail via google and btyahoo through google. went on holiday it was working fine on getting back i get server does not recognise my e-mail addresses error code 5.7.1 authentication

i have a iMac 27" using OS X Yosemite 10.10.2 since Feb 2015 i have been unable to send mail via the Mac Mail app no problems if i go into google and use my addresses via google i have tried all the fix's i have been able to find to no avail. the error message is server requires authentication error code 5.7.1 my server for mail is i think BT plc which is the largest phone and internet supplier in the UK i have 3 Smtp ports in use 25,465,587, this problem has now spread to my iPad which till last night had sent and received mail no problem.

ideas/ solutions would be apreasiated

it seems that after a upgrade these days you get problems ???