Yours sincerelly is rather used in British English. It is also used in the US, however, American speakers tend to reverse the order and use the expression as Sincerelly yours. If the name of the recipient is not known, Yours sincerelly is used but if it is known, Yours faithfully is better to chose. You can say goodbye at the end of a letter with Yours faithfully if it is rather an official letter, in case of a rather friendly but not intimate letter, you can use Yours faithfully. For example, if you use Dear Mr Smith to begin your letter, it is advisable to finish it with Yours sincerelly. If you began it with Dear Sir or Madam, for instance, you shall finish it with Yours faithfully.
