First, why 15 years? Why not 13 or 17 or 21 or 33? Or 42? Or 100? Or perpetuity?
Anyway, it is impossible to answer your question since it depends on the TLD of your domain name. Each registry is free to set up the rules that govern a domain name cycle.
If you have gTLDs in mind, registries are under contract with ICANN which sets many rules, including a limit here. Have a look at the Base Registry agreement here: https://newgtlds.icann.org/sites/default/files/agreements/agreement-approved-31jul17-en.pdf and its section 2.10:
Registry Operator shall offer registrars the option to obtain initial domain
name registrations for periods of one (1) to ten (10) years at the discretion of the registrar,
but no greater than ten (10) years.
And further below you have the same rules for renewals plus the fact that a domain name can never be expiring more than 10 years in the future (which could happend if you apply the other rules like you register a domain name for 10 years and then you renew or transfer it that would have added time but the other rule is to cap at 10 years maximum delta between now and the domain name expiration).
Many ccTLDs are following the same rules, so 10 years is often a maximum you will see quoted but it is absolutely not a technical limit.
Other TLDs may impose rules not so related with dates but with usage, especially in the free domain name market. For example in
.TK the creation and renewals are from 1 to 12 months, and you are forbidden to use it for web parking pages or non-existing pages (see http://www.freenom.com/en/dottk_contentpolicy_version21.pdf)
But there is a “catch”.
Everything detailed above relates to registries. But most often (there are exceptions), you do not buy your domain name at registries but at registrars. They are free to have their own rules, and for example they can sell you a service where they will take care to renew the domain for you for some amount of years if you prepay them. So they can go far above the registry limit of 10 years… but if they disappear the money you gave them disappear also and you will have no way to enforce it at the registry level… same if you transfer it elsewhere. Also what will appear in RDDS (Whois + RDAP) or in escrow files will always be the registry expiration date caped at 10 years in the future for example for gTLD and even the expiration date from the registrar will show the same and not the whole amount of years you paid.
Network Solutions for example claim to register domains for 100 years, see https://www.networksolutions.com/domain-name-registration/popup-100-yr-term.jsp
There may be others, but this is not very common.
And to slightly amend @dan comment, someone can also hear that the expiration date of a domain name is taken into account, because one can imagine that a spammer/low quality producer/Google algorithm player will be less likely to register a 10-years domain name than a 1-year one (because of course the costs is higher). But this is all speculation.
Note also that they are various initiatives that track “fresh domain names” to apply to them penalties in various red/black/white/green/multicolour lists of domain name reputations, used by various tools, such as anti-phishing, etc. So in that sense I concur with @dan on the fact that what matters more is since how long the domain exist, not when it will expire.
PS: it is silly to try to reverse engineer the Google algorithm (especially when “hearing” some argument from unknown sources) to find one criteria that would “boost” your ranking. Instead, focus on providing an high quality website with useful content and clear navigation, that will make your visitors happy and drive more traffic.