since five years ago.

1a. Things have changed since five years ago.
1b. Things have changed since five years.
2a. Things had changed since five years ago.
2b. Things had changed since five years.
3a. Things have been changing since five years ago.
3b. Things have been changing since five years.
4a. Things had been changing since five years ago.
4b. Things had been changing since five years.
Please correct and comment.
Thanks.

All the sentences without ‘ago’ are not correct.
Without ‘ago’ you would need to use
Things have changed in the last five years, etc. instead.

‘ago’ indicates that the starting point for the period under discussion was five years back from the present.

Beeesneees,
As per grammar book ‘ago’ is always used with past tense only.
How we can use ‘ago’ in present perfect tense as stated below:
“Things have changed since five years ago.”
Please explain the nuance of grammar involved here.
Thanks.

The best way to use ‘since’ and make it acceptable would be to mention the actual year, and say: Things have changed since 2011.

Note that ‘since’ refers to a particular point in time as in the recast sentence above. If you are not sure of that point, you can use ‘for’ which refers to a particular period as in ‘Things have changed in/for the last five years’. Here, in your sentence, the concepts of ‘point’ and ‘period’ of time are in conflict. However, if you still want to use ‘five years ago’, you may say: Things started changing five years ago, which means ‘Things started changing in 2011’ or ‘Things have changed since 2011’.

Look at these again:

I appeared on this forum five years ago.
I appeared on this forum in 2011.
I have appeared on this forum for five years (now).
I have appeared on this forum since 2011.

(I hope I haven’t confused you)