] Anielka,is it possible to explain in simple words for one who isn't familiar with the English(or American) terms what a "fifth cousin twice removed" means?

I forgot that most people don't know these terms any more!

Removal
"Removed" is just a generational term. Your mother's first cousin is your first cousin once removed in the ascendant

Ascendancy or descendency just means whether the generation from which you are removed is up or down. So for example, most people know that JA had a first cousin Eliza Hancock, daughter of JA's aunt Philadelphia Austen who was sister to JA's father, George Austen.

JA's first cousin Eliza Hancock had a son Hastings de Feullide. Hastings could correctly refer to JA as his first cousin once removed in the ascendant.
JA could correctly refer to Hastings as her first cousin once removed in the descendant.

Second and third cousins etc.

Most people know that first cousins, such as Fanny Price and Edmund Crawford share grandparents. Fanny's mother and Edmund's mother were the Ward sisters so their grandparents, Mr. and Mrs. Ward were common to both Fanny and Edmund.

Second cousins share great-grandparents. Imagine your grandfather had a brother. His grandchildren would be your second cousins.

Third cousins share great, great grandparents etc. etc. (One day I will learn to use HTML and get some server space so I can post diagrams- meanwhile, a pencil and paper may help you with the following:-)

So for example, JA's great, great grandparents were Sir James Brydges and his wife Elizabeth.

They had a daughter called Hon. Mary Brydges who was JA's great grandmother and a son called James Brydges, first Duke of Chandos. The Hon. Mary Brydges and James Brydges, first Duke of Chandos were brother and sister and shared parents (Sir James Brydges and his wife Elizabeth).

The Hon. Mary Brydges had a son called Thomas Leigh whilst her brother, James Brydges, first Duke of Chandos, had a daughter called Lady Caroline Brydges. Thomas Leigh and Lady Caroline Brydges were first cousins and shared grandparents (Sir James Brydges and his wife Elizabeth).

Thomas Leigh had a daughter called Cassandra Leigh whilst his first cousin, Lady Caroline Brydges, had a son called James Henry Leigh. Cassandra Leigh and James Henry Leigh were second cousins and shared great grandparents (Sir James Brydges and his wife Elizabeth).

Cassandra Leigh had a daughter, JA, whilst her second cousin, James Henry Leigh, had a son, Chandos Leigh. Chandos Leigh and JA were third cousins and shared great, great grandparents (Sir James Brydges and his wife Elizabeth).

Hope this is clear. It's as simple as I can without being able to insert a diagram! JA and her family would all have known this stuff automatically and would have been able to calculate the relative "nearness" of a family member almost without thinking about it.