Five Kingdom Classification

In Whittaker's five-kingdom classification, organization complexity increases from: C (Monera, unicellular prokaryote) \rightarrow E (Protista, unicellular eukaryote) \rightarrow A (Fungi, multicellular loose mycelium) \rightarrow D (Plantae, tissue/organ autotrophs) \rightarrow B (Animalia, tissue/organ/organ-system heterotrophs).

Whittaker's criteria were cell structure, body (thallus) organisation, mode of nutrition, reproduction and phylogenetic relationships.
Presence or absence of a well defined nucleus was not listed as a separate criterion.

In Whittaker's five-kingdom classification, all unicellular eukaryotic organisms are placed in the kingdom Protista.
$Chlamydomonas$ and $Chlorella$ are unicellular, eukaryotic green algae, so in this system they were brought together with $Paramoecium$ and $Amoeba$ under Protista (NCERT states this directly).
Monera contains only prokaryotes (bacteria and cyanobacteria), so it cannot include these eukaryotic cells.
Plantae contains multicellular, eukaryotic, chlorophyll-bearing organisms; 'Algae' is not a kingdom in the five-kingdom system.
Hence $Chlamydomonas$ and $Chlorella$ are included in Protista.

R. H. Whittaker (1969) proposed the five kingdom classification: Monera, Protista, Fungi, Plantae and Animalia.
His criteria were cell structure (prokaryotic or eukaryotic), body organisation (unicellular or multicellular), mode of nutrition, reproduction and phylogenetic relationships.
Among these, the mode of nutrition is the main basis that separates the three multicellular kingdoms: Plantae (autotrophic, photosynthetic), Fungi (heterotrophic, absorptive) and Animalia (heterotrophic, ingestive).
So, as per the answer key, the main basis of the five kingdom system is nutrition.