Ok let's break this down. First let's look at the tt you picked out. The 2104s mini lite (TT) has a dry weight of 3865 lbs and a cargo capacity of 943 lbs which gives it a gvwr of 4808 lbs. Ideal tongue weight is 13-15% of loaded tt weight. In this case we will use gvwr to calculate a tongue weight of 625-721 lbs.
Now let's talk about your Santa fe. We don't have enough info to tell you yes or no but here is how to figure it out. Ideally if you can go weigh your Santa fe (TV) with a full tank of fuel and all passengers,pets and cargo you intend to have in it when towing. Look for a cat scale
in your area or you can try a local feed store or dump for a scale. You want to weigh each axle separately but also get a combined weight. At a cat scale this can be done by putting front axle on pad 1 and rear axle on pad 2. Now take your total vehicle weight and subtract it from the Santa fe's gcwr to get your adjusted towing capacity (this will likely be lower than the quoted 5000 lbs). Next take your total vehicle weight and subtract it from the gvwr to get your available payload. Your tongue weight must be less than the available payload. Now subtract the rear axle weight from the grawr to see how much room is available on the rear axle.
If you are unable to weigh then go look inside your drivers side door for a tire loading sticker. It will say occupants and cargo should weigh less than x pounds. This is before the weight of passengers, pets, gear, etc. Subtract the weight of those items and people and you will get a poor man's version of available payload.
I'm betting this trailer will be over on one or more specs for your Santa fe. I would go smaller/lighter.
By the way, trailers come with the brakes on them, you need to have a brake controller installed on your Santa fe if you don't have one already. A proportional brake controller like prodigy P2 or P3 is recommended if you don't have a factory integrated brake controller. You need a seven round connector for the trailer pig tail to connect into.