The 6 is going to have 2 year old dated specs in about 5 months, go with the 5SE with better internals!
Best phone to get is the 6S or wait for the 7 in September.
Edit: Oh, you're asking about the 5S and not 5SE... The 5S is trash now, it's super old and slow. Not worth it, even if its free.
Ive had both and now I have the 6s Plus. The latter one being the best one for me tbh. Otherwise I should go for 6, only if it were for just some minor improvements.
Is a 6s in your budget? Because it's so much better, esp. the camera. If not the 5s or SE. Because I don't see much of a change in the 5s to the 6, but if you want the latest get the 6. Also look at the size, I held a 5S, 6, and a 6 Plus, and the 5s feels so small it's actually weird.