Is the 5000 view threshold a server side issue or a client side? In other words, would I be wasting my time creating a client side custom "view filter" from the Allitems list it's still going to process the 5000 then filter? I'm trying to filter by FY and the OOB view filter won't allow me to do it. So I'm thinking of creating a custom one.
The List View threshold is set per web application within Central Admin. If you navigate to Central Admin > Application Management > Manage Web Applications > Select your Web App > General Settings > Resource Throttling. You can increase the value here, but increasing this value will create overhead to the server. You can read this article, to know more about what happens if you increase the value and how it affects the performance.
Just a few common pieces of functionality that will break the list view include:
List Views that Group By a field
List Views that Total or Sum fields
Lookup Fields that use lists with more than 5,000 rows
Filtering a list view (unless fields are indexed)
Accessing data with the Client Object Model or REST
Why is 5000 ?
To minimize database contention SQL Server, the back-end database for SharePoint, often uses row-level locking as a strategy to ensure accurate updates without adversely impacting other users who are accessing other rows. However, if a read or write database operation, such as a query, causes more than 5,000 rows to be locked at once, then it's more efficient for SQL Server to temporarily lock the entire table until the database operation is completed.
Have a look at this article to manage the list view threshold limits.
The list view threshold is a server side issue. You can change it in CA while it is not recommended behavior unless you are positive that it will not negatively affect your system. Just like Karthik said, is is a by-design setting concerning back-end database. Here is an article you can have a check.