Years is or years are?

We can count years, can't we? But why is my answer wrong? This student had selected are in a practice question that goes like this:

(1) Five years (is, are) a long time to spend in jail.

His confusion is understandable. After all, the word year is a countable noun like dog and chair and behaves the same way in determiner-noun agreement:

(2) one dog/year, two dogs/years
(3) this dog/year, these dogs/years

And grammar rules on subject-verb agreement say use a singular verb for a singular subject and a plural verb for a plural subject:

(4) One dog is/was missing.
(5) Two dogs are/were missing.

So when he sees the plural years, he wrongly applies the subject-verb agreement rule to produce an awkward sentence below:

(6) ?Five years are a long time to spend in jail.

But the word years is a different animal, though it shares certain agreement and inflectional properties with other count nouns.

Whether the time word takes a singular or plural verb depends on its meaning in the particular context rather than on the presence of any grammatical marker. In other words, agreement according to the principle of notional concord.

When used to refer to a period of time, it takes a singular verb:

(7) Five years is a long time to spend in jail.
(8) Ten years was the time he took to build the robot.

When referring to more than one entity, it takes a plural verb just like other plural count nouns:

(9) Two years are added to the training programme.
(10) The next three years are going to pass quickly.

Besides years, other plural unit words involving money and distance also obey notional concord:

Money
(11) Forty dollars is a good price. (one entity)
(12) Two dollars are on her study table. (more than one entity, like two pens)

Distance
(13) Ten kilometres is not that long. (one entity)
(14) Five miles are to be added to this road. (more than one entity)