The question is not so much "When you need to renew it" as "Do you need to renew it" for that trip. And yes, you do.
You wrote "May 2026" for the travel date, without a day. Let's say you intend to go to the EU on 1 May 2026 and leave on 8 May 2026. In that case your current passport would fail both tests:
- It will be more than 10 years old on 1 May 2026 (it will 10 years and 10 days old).
- It will have less than 3 months remaining on 8 May 2026 (in fact just 13 days).
You also couldn't travel to the EU on 14 March 2026 and leave on 21 March 2026, because while your passport would pass the first test (it has not yet reached its 10th birthday), it will fail the second because on your intended day of departure it will have only two months of validity left.
Let's try travelling to the EU on 10 February 2026 and leaving on 18 February 2026. Here your passport is OK on both rules. On 18 February it will have more than 3 months left (21 May is more than 3 months after 18 February).
(Aside: The rules (Regulation (EU) 2016/399, aka the Schengen Borders Code) do not define whether 3 months means "90 days" or "the same numbered day in the third month after this one". I suggest you don't try to find out the hard way.)
Once the last of the UK passports that were issued with more than 10 years of validity on them have expired, which I think will be in 2027, the first EU entry rule ("Must be less than 10 years old on the day of entry) will become obsolete (at least for UK passports; I don't know if any other country has the same issue). At that point, any passport that passes the second test ("At least 3 months remaining on the date you plan to leave") will automatically pass the no-more-than-10-years-old rule.
This requirement to have time on your passport after your planned departure date is very common. In some countries you need six months on the date you arrive, and in some others you need six months after you intend to leave. So while a passport is officially valid for 10 years, in practice it can often only be used for travel for 9½ to 9¾ years.