What band pass filter should I use?

Question

C++ / C#

Task: in "real time" (that is, with a minimum delay), select a given band from the audio signal (for example, from 5 kHz to 10 kHz) and suppress the signal outside this band. Since the task is real-time processing, I take the buffer as little as possible (128 samples at a clock frequency of 44.1 kHz) and for the same reason I cannot accumulate several buffers or make a large delay line.
I know that in an audio editor (Adobe Audition or similar) you can apply an FFT filter. It allows you to clearly highlight the desired band, with a flat frequency response in the passband, with the maximum steepness of the transition band and complete suppression in the suppression band, and, in addition, undistorted sound: But this is a recording conversion when you can take, say, 4096 points for FFT.
Now I use a FIR (FIR) filter of the order of 30-50, the frequency response in the passband is uneven, the transition bands are large:
When you try to increase the steepness (order and delay line) of this FIR filter, the sound begins to be strongly distorted.
Which solution can be chosen for "cool" real-time filtering? Could an IIR filter be a better fit? If so, which one? Or choose a different impulse response for my filter?

Answer 1

Well, FFT and apply. First FFT, then inverse FFT only for frequencies of interest.
Intel MKL even has a Fourier Transform library optimized for Intel.