Once again, I think people are caught completely in the myth of large relative differences of small numbers, and the complete unawareness of how large and diverse the US is on many fronts.
Let’s look at some other 1997 data. State by State. Mind you, many States in the US are quite a bit larger than many entire countries in Europe.
1997 Utah Data:
http://hlunix.hl.state.ut.us/matchiim/main/infntdth/home.htm
Utah: 5.8 per 1000.
Wait - Utah too small for you? Let’s try California.
http://www.dhs.cahwnet.gov/hisp/chs/OHIR/vssdata/2000data/00Ch4Excel/1Reorg.xls
Oh, I see they were at 5.9 per 1000 in 1997. The same number as England in that year. And California is pretty close to equivalent population too.
And both of those States are larger (one physically, the other in both population and area) than Ireland, and both have a lower rate in 1997.
But how can that be?

Sure, there are lots of States with high rates. Some that exceed 9.0 per 1000, which is higher than most European countries. But…surprise! This is a big place, with a wide variation in demographics, poverty levels, climate, ethnic background, and history. The fact that I have to explain this again and again, especially to people who allege they are in the US, is most disturbing.
I do not think many understand the fact that we have, at least roughly, a Federalized nation. Our States are not in the least bit akin to counties in the UK - Kansas is not even close in its sovereignty and powers to Hertfordshire, say. Kansas, like most States, is effectively a country within a country. And the sooner people come to grips with that fact, the sooner they can start to talk intelligently about the US and its internal policies.
But let’s look at 2000 figures:
California: 5.8
England: 5.6
Ireland: 5.62 (2000 est)
Northern Ireland: 6.4 (1999 figures)
Texas: 6.4
I would say California compares well with England and Ireland, which are both enlightened countries which do not neglect their children like the US is alleged to do so. And even Texas in 2000 compares with the 1999 estimate of 6.4 for Northern Ireland. Imagine - Texas, the land of Bush the Evil, comperable with part of Western Europe on the subject of child mortality.
Note I called out what was an estimate and what was a different year. That’s because I’m trying to be as accurate and truthful as possible here. You don’t address or solve problems by pretending they aren’t there.
But is there a “problem”? 
And admittedly, I am picking and choosing some key States to make a point. So let’s look at the range in 2000.
And bringing up the front for the US, is:
New Hampshire: 4.3. Gee, that’s pretty good, don’t you think? They must be doing something right.
and in last place, is:
Mississippi: 10.4 Wow - that really sucks. That’s a shitty rate, and one which says something is seriously wrong there.
I am still waiting for those cites on how the quality of the US health care system is comperable to Cuba’s. How long should I wait again?