Should I get an Audi TT as a first car

I would look at insurance first before purchasing, as you might find out the insurance will be far higher than what you paid for the car. I can't recommend a car someone else will, but insurance wise, I can tell from your age, and your first-time car will be high.
Best look at insurance comparison sites to see for yourself.

First-time new driver plus age, also it would depend where you live and where you will keep it at night would also matter as well. I would say around 3k. For a sports car, maybe 4k or higher.
In my experience, I paid around £800 without a blackbox, with £1500 for a 2 litre SUV

Black box insurance - also called telematics - is a type of car insurance which sees a small device fitted out-of-sight in your car and it measures how well you drive in order to reward safe drivers with discounted insurance.
For me it wasn't worth the price as for my situation it was more expensive. In your case it can be cheaper but you need to look on your comparison websites for your situation, I can't give you a fixed number as everyone's situation is different.

Black box insurance - also called telematics - is a type of car insurance which sees a small device fitted out-of-sight in your car and it measures how well you drive in order to reward safe drivers with discounted insurance.
For me it wasn't worth the price as for my situation it was more expensive. In your case it can be cheaper but you need to look on your comparison websites for your situation, I can't give you a fixed number as everyone's situation is different.

I think it also needs to be made clear that they have the ability to cancel your insurance based loosely on the data they get from the box and you don't really get much appeal which leads to a lot of controversial cancellations (and is a large part of why I would always pay for full cover rather than cheap out)

I can't really recommend it, as you'll be paying a pretty high insurance for a premium car + new driver, and Audis of this age are cheap for a reason, most are over 100k miles and getting to the point where they need some expensive servicing - timing systems, clutch, transmission, brake kits, subframes etc, most costing over £1000 as these cars aren't cheap to work on. I've owned both an 06 & 08 Audi and the 08 is off the road while I save £2000 for a new clutch 😅

Are you ready to pay the pretty high insurance cost for your first sports car? Some insurance companies might not even cover it, so you may need to look for something else.
Have you looked at insurance comparison sites to see if it's in your ballpark financially? I'm asking so you won't get a surprise on how high it would be.

I have found so many cheap, second-hand Audi TTs from 2010 for about 3k. I will be 19 when I look to get my first car. I really want a sporty and good-looking car for under 5k and the Audi TT seems good. What do you lot recommend and would insurance be too high?

Id get a few car insurance quotes to see what the insurance is likely to be like before doing anything.
Car insurance can be a bit horrific at the best of times for young drivers, even for normal/basic cars. It can be even worse for cars that are sporty etc.

Have you decided what car you're going for? So we all know if you have changed your mind on a sporty car.