I need to provide the ability to get a customers most recent order.
Of course you could provide query parameters to filter, sort and slice the orders collection, but why not making it simpler and give the latest order if the client needs it?
You could use something like (returning a representation of a single order):
GET /customers/{customerId}/orders/latest
The above URL will map an order that will change over the time and it's perfectly fine.
Say there is also a case where you need last 5 orders. How would your route(s) look like?
The above approach focus on the ability to get a customers most recent order requirement. If returning the last 5 orders requirement eventually comes up after some time, I would probably introduce another mapping such as /recent that returns a representation of a collection with the recent orders and accepts a query parameter that indicates the amount of orders to be returned (5 would be the default value if the parameter is omitted).
The /latest mapping would still be valid and would return a representation of the very latest order only.
Providing query parameters to filter, sort and slice the orders collection is still a valid approach.
The key is: If you know the client who will consume the API, target it to their needs. Otherwise, make it more generic. And when modifying the API, be careful with breaking changes and versioning the API is also welcome.