To answer your title question, the Pāṇḍavas just wanted one village each.
Yudhishthira said, "O Sanjaya! ... Then you should repeatedly speak to
the intolerant Prince Suyodhana, entreating him when he is seated in
the midst of the Kurus. When Krishna was brought alone into the
assembly hall, evil was done towards her. But we ignored it patiently,
so that the Kurus might not be slaughtered. The Pandavas have borne
hardships earlier and will do so again, though they are stronger now.
All the Kurus know this.
'O peaceful one! You sent us into exile, with
deerskin as our garments. We bore those miseries, so that the Kurus
might not be slaughtered. When Duhshasana, with your approval,
oppressed Krishna by the hair in the assembly hall, we overlooked that
also. O scorcher of enemies! But we will fight for our rightful share
now. O bull among men! Turn your mind away from avarice and from
grasping the possessions of others. O king! Let there be peace and
harmony amongst us. We wish for peace. Give us one province from your
kingdom—Kushasthala, Vrikosthala, Asanti, Varanavata and whichever
else you pick as the fifth and the last. O Suyodhana! Give five
villages to the brothers.'108
O Sanjaya! O immensely wise
one! Let there be peace between us and our relatives. Let brother be
united with brother, and let father be united with son. With smiles,
let the Panchalas mingle with the Kurus. I desire to see the Kurus and
the Panchalas uninjured. O son! O bull among the Bharata lineage! Let
all of us live happily in peace. O Sanjaya! I am as ready for peace,
as I am for war. For the sake of dharma and artha, I can be mild. But
I can also be terrible.
108 One village for each of the five Pandavas.
(The Mahabharata: Volume 4, Bibek Debroy)
As for why only those five villages, no reason is given in the Mahābhārata.
However, V. R. Narla in his critique The Truth About the Gita: A Closer Look at Hindu Scripture conjectures the following on why two villages in particular made it to that list.
Had he not enough influence with the Pandavas to ensure a peaceful settlement of their dispute with the Kauravas? Why did he not use it to that effect? True, he went as an envoy of peace to Hastinapura. But why, then, did he present unacceptable demands in the guise opting for the barest minimum? The popular impression is that the Pandavas were prepared to give up their claim to their half-share of the kingdom, provided they were offered five towns together with their hinterland. But what is forgotten is that two of them were snatched by Drona from his boyhood friend and later enemy, Drupada. Being honorable men, how could the Kauravas ask their teacher Drona to give up his possession so that they could make peace with the Pandavas? Krishna was well aware of this and yet he did his best to paint the Kauravas as so proud and power-drunk as not to agree to the lowest minimum terms in the interests of peace.