What is the functional and structural distinction between core (H2A, H2B, H3,H4) and linker(H1/H5) histones?
The core histones are H2A, H2B, H3, and H4, and the linker histones are H1 and H5. The structure of the nucleosome is well explained in wikipedia:


  Two of each of the core histones assemble to form one octameric nucleosome core particle, and 147 base pairs of DNA wrap around this core particle 1.65 times in a left-handed super-helical turn. The linker histone H1 binds the nucleosome and the entry and exit sites of the DNA, thus locking the DNA into place and allowing the formation of higher order structure. The most basic such formation is the 10 nm fiber or beads on a string conformation. This involves the wrapping of DNA around nucleosomes with approximately 50 base pairs of DNA separating each pair of nucleosomes (also referred to as linker DNA). The assembled histones and DNA is called chromatin. Higher-order structures include the 30 nm fiber (forming an irregular zigzag) and 100 nm fiber, these being the structures found in normal cells. During mitosis and meiosis, the condensed chromosomes are assembled through interactions between nucleosomes and other regulatory proteins.


The core histones have a positive net charge, which facilitates the interaction with the negatively charged phosphate groups of DNA. 

Apart from defining the nucleosome structure, the function of the core histones is regulatory: it can switch on/off gene expression by histone modifications like acetylation or methylation. 

The gene expression is ON when there is:

• DNA demethylation

• histones acetylation
• H3K4 methylation
• H3K36 methylation

• H3K9 demethylation
• H3K27 demethylation

The gene expression is OFF when there is:

• DNA methylation
• histones deacetylation
• H3K4 demethylation
• H3K36 demethylation
• H3K9 methylation
• H3K27 methylation

// H3K4 demethylation is abbreviation for: Lysine 4 of H3 is demethylated.

Berger SL. 2002. Histone modifications in transcriptional regulation. Current Opinion in Genetics &amp; Development 12: 142–148 is also a nice review.