Fifth harmonic generation (5th HG) of a Nd:glass laser is an effective way to acquire high-energy coherent deep-ultraviolet radiation near 200 nm. In this work, cascade generation of the fifth harmonic of a Nd:glass laser in a 5 mm ammonium dihydrogen phosphate (ADP) crystal was investigated, and maximum conversion efficiency of 14% and large angular acceptance of 45 mrad were demonstrated at a noncritical phase-matching temperature of 75.1°C. However, as the results reveal, the temperature sensitivity and nonlinear absorption would hinder its high-energy application. As for that, based on the complementary relationship of the angle and temperature in the phase-matching condition, an upgraded focusing 5th HG design coupled with the cylindrical temperature distribution scheme was proposed. By this upgraded focusing design, more than the improvement of the conversion efficiency, the output 5$\omega$ near-field intensity distribution turns out to be insensitive to the temperature gradient. Potentially, this idea can be applied for many other frequency conversion schemes such as high-repetition frequency lasers, which have similar temperature gradient problems.