In this paper we present a high resolution IR spectrum of the planetary nebula Hb5, over the range 1.6-1.75 micron. Our aim is to test the hypothesis invoking emission from upper vibrational levels in excited PAH molecules and anharmonicity of the C-H stretching mode to explain the weak features observed in the 3 micron range. The predicted first harmonic of the 3.3 micron band at 1.67 micron has not been detected. The upper limit we set indicates that his band must be at least 45 times weaker than the 3.4 micron feature. This, together with the high value of the F(3.4)/F(3.3) ratio, challenges the assumption that the 3.4 micron band is the first hot band.