I've built lots of things.
Recently though, I've had builders building red brick cavity walls to approx your dimensions.
One was a skilled bricklayer - the other an experienced builder - and a labourer using a cement mixer to keep them going with mortar.
On the basis of what they did for me, it would take a skilled bricklayer and a full-time labourer maybe two full days to build a 12 x 5 wall.
Without the cement mixer and labourer - ages!!!
A 12 x 5 wall is more than big enough to catch the wind and blow over in one piece - as you see every year in winter storms news reports when it lands on a car/person etc.
If it's on public view you will probably be worried about appearance.
My builders stopped when they got about half way up to allow the mortar to dry for the next day - otherwise the weight may compress and distort the construction.
On a personal note I've always found getting the correct mortar mix very difficult: soft enough to be malleable, not so soft that it runs off the brick.
Getting the mix consistent so that the same break doesn't compress the mortar differently along the length of the wall.
If it was just a barbecue, I'd do it but a high wall on public view - nah.
Without a cement mixer you will kill yourself too. That's a lot of sand and many, many bags of cement.
Good luck .... perhaps some photos afterwards 