For 'regular' licences (i.e. permanent ones) there are two distinct types. Each pub (for example) must have a premises licence AND at least one person running the pub must hold a personal licence. When trying to make sense of the TENs rules, you need to split the two types of licence up in your mind.
Let's say that you, Eve1974, want to hold a licensable event in your local village hall, which doesn't have a premises licence (and there's not a personal licence holder available to take charge of such events there):
You, as an individual, can only have your name on 5 TENs per year. They might all be in your local village hall but, if you so chose, they could be in five different village halls.
Your local village hall is considered as a premises though. Other people might want to apply for TENS there but the limit for events covered by TENs in that hall is 15 per year.
So the limit of 5 TENs applies to you, whereas the limit of 15 TENs applies to your village hall.