BigQuery : Regex after a string

How can I do that?

works in both BigQuery dialects: Legacy and Standard SQL

SELECT 
  REGEXP_EXTRACT('source:destination:city:street:number', r'(?:.+:){2}(.+)(?::.+){2}')  

see more for REGEXP_EXTRACT and re2 syntax

if I need the first word after source: for example?

SELECT 
  REGEXP_EXTRACT('source:destination:city:street:number', r'(?:.+:){1}(.+)(?::.+){3}')  

There are many options here for you depends on what exactly you need
Another one is below (BigQuery Legacy SQL)

SELECT 
  NTH(1, SPLIT(text,':')) AS source,
  NTH(2, SPLIT(text,':')) AS destination,
  NTH(3, SPLIT(text,':')) AS city,
  NTH(4, SPLIT(text,':')) AS street,
  NTH(5, SPLIT(text,':')) AS number
FROM (
  SELECT 'source:destination:city:street:number' AS text
)