That's so cute. I wish I could adopt another cat.
I don't know whether it is different between two cats but I followed the recommended way of introducing animals to one another when I introduced my kitten to my rabbit last month; this technique involves setting up a room for the new member so that he will have plenty of hiding places. Make sure to leave some food, water, and a litter pan in that room. Leave him in that room alone to explore for a while (a few minutes, an hour or two)
Your cat might be scared for some time so it's best to introduce every member of the family slowly, including your 5 month old cat. You should bring your older cat to meet the new cat in that room you set up, hold the 4 month old while someone else holds the 5 month old and let them smell each other. Then let the younger cat walk up to the older one. If you feel like they aren't going to attack one another, release both of them and watch them carefully. Any sign of trouble, separate the two and wait a few hours or another day to reintroduce. Do this until they've properly been introduced.
It didn't take too long for my cat to be okay with my rabbit. It only took about 4 days. She hid a lot during that time.
(I did have to do this introduction with 2 cats a long time ago but it went without a hitch. That was 10 years ago. Can't remember the trick(s) I used there) Good luck to you and your cats.