Hello there, im trying out this from a workbook,I have no one to explain to me.

Could someone tell me the proper procedure of of laplacing this? it seems it is using the function of multiplication t, which is -F'(s) , but not as near to the answer(attached), could someone explain to me? especially the extra +(5/(s-1)) value which i dont think it comes from partial fraction. Thank you, kamsahamnida.