HZ123,
On the old low-bypass engines there was a real danger of a rich blowout at acceleration. Meaning too much fuel could cause a flame-out. So acceleration was slow, probably around the numbers you quote.
However, on newer engines, both low- and high-bypass, that is much less of a problem, so you can just about cut the 13 seconds in half or more.
I have done quite a few acceleration checks, both after engines changes and on test flights, but I can't for the life of me remember any numbers at the moment. But 4 to 5 seconds seems to ring a bell.