We review recent results on near-horizon static black hole solutions and entropy in R 2 -corrected N = 2 SUGRA in D = 5, focusing on actions connected to heterotic string compactified on K3×S 1 . Comparison with α ′ -perturbative results, results obtained by using simple Gauss-Bonnet R 2 -correction, OSV conjecture and microscopic stringy description (for small black holes) shows that situation in D = 5 is, in a sense, even more interesting then in D = 4.Copyright line will be provided by the publisher 1 5-dimensional black holes in higher derivative N = 2 SUGRA Bosonic part of the Lagrangian for the N = 2 supergravity action in five dimensions is given bywhere A 2 = A α i ab A i ab α and v 2 = v ab v ab . Also,A bosonic field content of the theory is the following. We have Weyl multiplet which contains the fünfbein e a µ , the two-form auxiliary field v ab , and the scalar auxiliary field D. There are n V vector multiplets enumerated by I = 1, . . . , n V , each containing the one-form gauge field A I (with the two-form field strength F I = dA I ), and the scalar M I . Scalar fields A i α , which are belonging to the hypermultiplet, can be gauge fixed and the convenient choice is given by A 2 = −2, ∂ a A α i = 0. Lagrangian (1) can be obtained from 11-dimensional SUGRA by compactifying on six-dimensional Calabi-Yau spaces. Then M I have interpretation as moduli (volumes of (1, 1)-cycles), and c IJK as intersection numbers. Condition N = 1 is a condition of real special geometry.