What is the limit on number of contacts in a distribution list, if any?
Per the help file:
“eM Client enables you to create a so-called distribution list, which is basically a list that can contain any number of contacts.”
Yes, as @sunriseal says, there is no limit in eM Client.
However, if the list is saved on a server, there may be a limit there. For example, the server may not allow a DL with more than 100 members, or it may not allow a DL at all.
Another thing to consider is that email providers often limit the number of messages you can send per hour, or the number of recipients you can have in a message. So if you setup a DL with 5000 members, you may not be able to use it.