let x be the positive number (x>0) and y the other number

one positive number is 5 more than twice another number

x = 5 + 2y

their product is 1272

x*y = 1272

plug x = 5 + 2y into the last equation

(5 + 2y)y = 1272

by solving we find

y = 24

click here to see the step by step solution of the equation

x = 5 + 2*24

x = 53

the numbers are 53 and 24.