website age is a one factor of authority. very little factor.
authority website that come in top of mind when you said a niche.
example : Internet marketing forum, in your mind will come up warriorforum
that's is called authority website, not only aged.

authority = knowledge

In other words, a 5 year old web site about grooming dogs with 10 pages of 400 words each, and several affiliate ads on each page, is going to rank VERY LOW in authority.

Whereas the 2 year old website about grooming dogs with 400 pages of 2,000 words each and only 1 or 2 ads on the entire site, is going to rank VERY HIGH in authority.

Things Google looks for when determining authority is:

• word count per article
• one primary keyword topic per article
• 4 to 10 secondary keywords that are synonyms of the first keyword
• site producing 1 to 5 new articles per week
• expertise of the author (in our dog grooming example: is the author a pet shop owner, professional dog groomer, or veterinarian, or is it just just random joe off the street with no credentials to back up his claims?)

When it comes to age, a site under 3 years old will always have difficulty ranking high on Google, simply because sites under 3 years old are prone to closing down/being abandoned, so the Google algorithm does not weigh young sites heavily in search results.

HOWEVER, just because a site is 5 years old, doesn't mean Google automatically boosts it's rank. The site has to have proven that it's webmaster is an authority of the topic in question.

In other words, let's say you build a site on diet and exercise, but you are just a person looking to push clickbank ads for a new diet pill, so you buy a domain that's 5 years old, hoping it's age will boost your rankings, then slap a few clickbank ads on it site and wait for affiliate income to come in.

Now, let's also say, that at the same time Richard Simmons, one of the world's top diet experts, also decides to build a website. He writes a few articles to promote his latest cookbook, and puts the site on a brand new domain with no age at all.

Who is Google going to rank as the authority site? The site created by the AUTHORITY IN THE FIELD - the dietitian, with several decades of experience in helping people one on one.

When Google's RankBrain looks for an authoritative website, it has nothing to do with age of the site, but the career of the site owner.

A doctor with a degree from Harvard, is an AUTHORITY in medicine, and his site is the one Google will rank far above any so-called "health" site run by a random guy off the street, no matter how old its domain name happens to be.

Age of the site becomes important only when two compatible sites (in other words TWO law firm sites run by two different law school graduates), then Google looks to see which site is older.

But comparing a random site on a random topic, to an authoritative site written by an expert in their career is comparing apples to oranges.

In other words, if you don't have a college degree to PROVE you are an authority in your field, you'll have a hard time convincing Google your site is an authority of it's topic.

The days when any body could write about any topic and rank high in search results are long gone. Google's RankBrain actually looks for experts who have a career and proven track record in their topic and promotes those sites first now. And as RankBrain gets smarter (it's an AI program) it'll just become that much more difficult for anyone without a college degree to rank in Google's search results at all.

Yes, it is unfair for those of us who do not have college degrees, but that is the way it is these days.

When Google says it wants AUTHORITY sites, they really do mean, sites written by authoritative, professional experts.

Nice question. Precisely
Domain Authority of a Website depends on various other factors irrespective of the domain age of a particular website. Domain authority has a ton of other factors beyond just domain age. Rand Fishkin from Moz actually did a great video on it. The age doesn't really count for much--it's the engagement (points) that counts and which helps to adds authority. Likewise, if your domain was registered back in 2006 but was not used until 2011, it would accrue age but not authority. Once the domain begins actively playing a role on the web and Google can measure that other domains and users are interacting with it, it may begin accruing authority.

No, you can't say about DA & PA if a website is 5 year old. It depend on how quality content & links that site have.

Website age refers to the length of time that a website has been registered and active.

Domain authority is a measure of the power of a domain name and it is based on three factors: Age, Popularity, and Size.

SO what role have backlinks in website authority?

Site age and domain authority have nothing to do with one another. They are completely different things. A site could be 30 years old and have little to no authority because it has thin or just plain bad content with no links (or worse, bad badlinks). A site could be six months old and have very good authority based on links and content.

Basically Google will access the value of your site primarily on its relevance to the search input. Google will attempt to present the most relevant pages first. How they are ranked to appear is a complex undisclosed algorithm.

One factor in this ranking is the authority and relevance of sites linking to your site pages. The DA & PA of these sites are calculated based on quality issues regarding once again on the perceived authority of content on that site including the authors credentials to place such content and indeed on user popularity of a site for a large number of searches showing real people visiting. This effects the DA.

This reputation aspect is important but the linking site value will be rated on how relevant the site content is to the linked page. And if the linking site has a high DA that helps even with a low PA link. It will be valued as a authority link if it provides authoritative relevant content to the topic content of the linked page.

The more authoritative and relevant sites that link to your site the higher your site will be ranked for the user search phrases that are most relevant to your content.

Google wants to mirror natural user behaviour in the way we value where we go on the web and what we consider as valuable in its search results. It wants to provide results that most people would consider relevant.