Well
Normally current density of a conductor considered as 5A/mm^2
It means 5A can easily flow a conductor having cross-sectional area of 1mm^2
Here your conductor is 38AWG or diameter 0.102mm
Area of conductor = 3.14*(.102/2)^2 = 0.0081mm^2
If 14 strand them Area = 0.0081 * 14 = 0.1143mm^2
So the current capacity = (5A/mm^2 )*( 0.1143mm^2) = 0.571A
Yes 14 strand wire of 38AWG will withstand 5A
The forum is not meant to let others do your job.
It's not more effort for you to do an internet search ... than for me.
The benefit if you do the internet search on your own is:
* you have the results more fast
* you may decide on your own if they are "reliable" for you, since I don't know your what "reliable" means for you.
There are many thousand results. Just go through a couple of them to find out what is the most suitable for you.
If there still is a question feel free to ask for help, but please post the link to the document of your choice...so we have the same source to discuss about.