A couple points are worth mentioning before a longer answer is provided.
First, the 95% number is probably not accurate. It gets quoted anywhere from 90% or more, but it's almost certainly fudged. It's very often brought into question, considering the one child policy doesn't apply to ethnic minorities, and population numbers in rural areas are pretty famously under-reported.
The other part of this is that the classification of Han, the majority ethnic group, may just as well be considered an umbrella term, covering a number of distinct ethnicities. You see distinct languages and cultures among the Wu areas, the ethnic Hakka, Yue peoples and so on. To say that 90+% of China is ethnically homogenous may well be based on a different resolution than to address the groups you have in mind elsewhere. There are historical, linguistic, cultural and genetic variations among the Han that could just as easily be considered separate but related ethnicities. The term "Han" is just as much a point of convenience as it is an objective reality.
That's not to say there's no such thing as Han. Genetic studies have shown shared ethnicity among those who'd traditionally be considered Han. Here's one such study (sorry, abstract only before the paywall) that addresses both similarity and difference among Han populations.
To add to that, here in Taiwan where a large population of modern inhabitants would be considered Han were they to go to China, the concept of a Han ethnicity is not widespread. People instead tend to identify as Hoklo (Min speakers), Hakka, Mainlanders (those whose families came to Taiwan around the time of the civil war) or Aboriginals (of which there are over a dozen different groups). Meanwhile back over in China, some of the official ethnicities have very short histories, and others still are highly questionable as far as how closely they reflect any sort of reality in cultural and genetic heritage (for example, each of the Taiwanese aboriginal groups, with separate languages cultures and in some cases origins, are grouped together as a single ethnic group called Gaoshan, according to the Chinese government).
Happy to provide sources on the above, if needed. Some of it is general enough I didn't bother in this first post.
edit: The language/dialect thing is getting out of hand in some comments. I'd like to try to cut off any further expeditions into nonsensery with the following:
Languages and dialects are distinguished largely on sociopolitical factors. There is no actual globally objective way to draw a line between the domain of the two terms. None. Any two related languages can just as accurately be called dialects or dialect groups of their common parent. English is a dialect group of Germanic, or Philadelphia English is a language in the English family.
Not all Chinese languages/dialects are written the same. It's a myth. It's possibly the most annoying myth we Chinese linguists encounter. Most people write in Standard Mandarin, regardless of what they speak. Think of it like Europe when people would publish books in Latin even though at home they're speaking some German of French dialect, and not really chatting up their pops in Standard Latin. There is written Cantonese and written Wu and written Hakka and it doesn't look like Standard Mandarin except that characters are being used. But then, not always the same characters. The word order is different. The vocabulary is different.
你知，佢係嘛个人？𠊎毋知。
侬晓得，伊是啥宁伐？阿拉勿晓得。
你知道，他是谁？我不知道。
That's Hakka first, then Wu, then Mandarin. All saying "Do you know who that is?" and "I don't know". They are not written the same. In China, they people do typically do their writing in Standard Mandarin, since it's the lingua franca. But if you go to places outside China where there are Chinese speakers, it's not at all uncommon to see non-Mandarin in writing. For example here in Taiwan I see written Hakka and Min pretty frequently, even on things like the labels on the produce printed out by the grocery store. But then even inside China you'll see it, and it's not too tough to go find literature in the other Chinese non-Mandarin languages.