8-9 is usually third grade, fifth grade is 10-11, and occasionally 12 year olds.
While far more rare, holding back or a school pushing for entry into a lower year group does happen in the UK. In the cases I know of, it was for children who had missed significant amounts of education mostly or a couple cases of families couldn't provide evidence of education who applied for entry to Year 10 by age where the school pushed for Year 9 entry. We also have schools with in with internal alternative provision where KS3 and KS4 children are being taught KS1 skills - and there is a massive growing need for this. All systems are trying to find ways to manage the issues around age not automatically meaning capability.
Many early schools in the US and elsewhere had children of different ages learning together and people passed up grades upon completion of testing, not by the calendar, and resources for additional support and spaces are slim so repeating was the most practical option.
It has grown much less common in the US the last few decades, as more places ban the practice for all but final year students, who may be required to repeat some classes or tests to meet school and state standards (though they may be encouraged to go the GED route instead, and may be required to do after a certain age). It's why there are so many US teachers complain about 'socially passing' children who have failed or school district policies refusing to allow children to be failed, the bans usually are implemented with the explanation of the social impact on children, though evidence-wise there is little support that simply repeating a year improves outcomes for most children without adding in additional support. I don't know of any school district that would enable 3 years of repeats, they'd usually then be moved into special education or alternative education routes well before that which works very differently in most districts I know. It's not unusual in some districts for those with significant additional education needs who can't be in their own grade academically to be in the same classroom with the same teacher the entire time they're at the school for academic or sometimes all subjects, so their actual grade doesn't matter that much.
There is no one US education system. Even within the same school district, it's possible for different elementary schools to have different entry requirements from birthdate cut off to developed school readiness skills (some kindergartens require kids to come in and demonstrate their skills before they can have a place). Different high schools, while having to meet state and local standards, will have different graduating requirements which can change each year. When I graduated, the grade before and after me had different state tests that had to be passed, and every high school in the city had different course requirements. There are state and local standards for content, but the curricula caries widely - I started high school at one where the maths were separate (Applied Maths, Algebra 1, Geometry...) and moved to a school where it was an integrated maths system more similar to the UK. There is also a growing trend in areas with local colleges or universities for high school students to do both high school and uni classes - some high schools even put university classes in their options for students now who can test in those programs.
International education studies do show that the US requirements in English and Maths for simply graduating are low compared to many other countries
I wouldn't argue that the US graduating standards aren't lower, it's fairly well known, it's why the US college system has general ed requirements and such a large community college and adult education system.
I would argue that international education studies have a very difficult time comparing very different systems and tend to rely on things like time required in education and state-required content for things like graduating requirements. This is why many countries, like all the nations of the UK, have bloated and pushed content down the curriculum in a dick waving contest among nations. It's similar to how nations including the UK changed the definition of how literate the population from how many can read and write to the amount of the population that has a certain number of years of schooling - it's not quite the same thing, but it's easier to compare. The US has also joined in on this dick waving, just more slowly.
More isn't always better. I personally prefer a lower level of content prioritised and focused on for general education that most of the general population use and can show they have attained than a higher level of content that give schools little breathing room and most are failing for little reason other than bragging to other countries. There is always a balance to be struck, but the US's 87% graduating with a high school diploma - requiring enough to pass 20-30 subjects well enough - does stand in contrast to less than 50% of English kids get a strong pass in English and maths GCSE. That schools can be rated good with 15% of kids meeting what is meant to be the basic standard boggles my mind.