Particle-$gamma$ coincidences from the $^{89}$Y($p,p gamma$)$^{89}$Y and $^{89}$Y($d,p gamma$)$^{90}$Y reactions were utilized to obtain $gamma$-ray spectra as function of excitation energy. The Oslo method was used to extract the level density from the particle-$gamma$ coincidence matrices. The impact of the $N=50$ shell closure on the level densities is discussed within the framework of a combinatorial quasi-particle model.