You can do the division in base 5; you just need to know how to do addition and subtraction in base 5.
Since you are not familiar with base 5, it helps to start by making a list of the multiples of 24 in base 5. Of course the work must be done in base 5; you can use either addition or multiplication to make the list. As a check of your work, you can show that in base 5 "24" times "5" is "240".
24*1 = 24
24*2 = 24+24 = 103
24*3 = 103+24 = 132
24*4 = 132+24 = 211
24*4 = 211+24 = 240
Now you have a list of all the multiples, in base 5, of the divisor, 24. Do the long division just as in base 10, remembering that the subtractions are in base 5.
32
------
24 ) 1423
132
----
103
103
---
0
1423 divided by 24 in base 5 is 32.