Prove Sum of 5s and 7s for n > 23

[ipitydatfu]

Question Details:
show that any number greater than 23 can be written as a sum of 5's and/or 7's


attempt:
24: 7 7 5 5
25: 5 5 5 5 5
26: 7 7 7 5
27: 7 5 5 5 5
28: 7 7 7 7
29: 7 7 5 5 5
30: 5 5 5 5 5 5
31: 7 7 7 5 5
32: 7 5 5 5 5 5
33: 7 7 7 7 5
34: 7 7 5 5 5 5

from this, i see that this follows a pattern:
n = f(a,b) = 5a + 7b

for n> 23


but how do i go about to prove this for all values?

 

[blinktx411]

Could you show that it was true for 24,25,26,27,28 then just say that every number beyond these can be expressed as x + 5n, where x is one of 24,25,26,27,28 and n is a natural number?

 

[ipitydatfu]

lol yeah. i kinda figured it out similar to that way after taking a long nap. thanks for the response though!