As you may have found, if you use augmentation, there isn't a way to make the new faces coplanar with existing ones.
However there's an easy way to create this model, using stellation.
Make sure you have a stellation view open:
Also select the option to show the stellation plane on the selected face, rather than just highlighting it:
Then when you select one of the triangular faces you'll see this:
Hold down Shift and look at the available mouse actions in the bottom right corner:
What you want to do is Shift+Right-click on the central triangle, to select the stellation cell above that triangle, which will add the pyramid you want.
Stellation is all about intersecting facial planes. Here, the neighbouring facial planes will extend over the triangle to enclose a region above it.
Do the same for the pentagon and you've got the model you wanted:
Finally, if you want, hit the left-and-down button in the top right corner of the stellation view to convert the stellation into the new base model:
