That's normal, and I dare say five seconds is on a good day and depends on your platform. BBC One HD on Sky is about eight seconds behind "real" time.
If you watched any of the new years celebrations from around the world on Sky News yesterday at the various top of the hours, it becomes apparent just how significant the delays are. Your wall clock says it's 1pm, the Sky News clock ticks over to 1pm about seven seconds later and Sydney continues to count down for another five seconds or so on the pictures after that.
You can measure the delay on BBC 1 and the NC when the sports news from Salford is on. You can just make out the digital gallery clock in the back ground. HD does indeed add another 2-3 seconds
Aren't the regional variants of BBC 1 all delayed with respect to each other on DSat to give the statmuxing a fighting chance? Plus obviously different lengths of circuit for the round trip to each regional centre.
Yes there are delays before the coders ...
but as the interstudio links are all ST 2022-6 there is no significant delay there.
( btw on an commodity MPLS from Aberdeen to goonhilly the delay is only 43ms...
BT M&B IP over optical is faster,!)