How to validate following string using regular expression - "4500788390 14-AUG-2017"

Try:

^\d{1,10}\s+\d\d-(JAN|FEB|MAR|APR|MAY|JUN|JUL|AUG|SEP|OCT|NOV|DEC)-\d{4}$

But ... it's a bad idea.
Use a regex to split it into the number and date portions:

^(?<Number>\d{1,10})\s(?<Date>\d\d-...-\d\d\d\d)$

And then use DateTime.TryParse or DateTime.TryParseExact to check and convert the date. Regexes are not good at verifying date info - there are too many exceptions!