Searching in a string with index

Hi,
When I search some words into a varchar column and this column has an index.
Does Postgres use index??

The search is done this way:

create table tb_gen_person (
  pes_nro_doc numeric(14) not null,
  pes_name varchar(150) not null,
  constraint pk_person PRIMARY KEY(pes_nro_doc)
);
create index ix_person_01 on tb_gen_person (pes_name);

select *
from tb_gen_person
where pes_name like '%albert%';

Not considering upper case, or tsearch2, this type of search use index
somehow?
I overhear that if the search has more than 5 characters, probably would
use index!! Is this true?

Thanks