2010 xIMC keystage2-EMIC individual Question 3

The notation $d_n$ means $n$ repetitions of digit $d$, with adjacent blocks concatenated. For example $5_3=555$, $4_3 9_5 8_1 3_6=444999998333333$. If $2_w3_x5_y+3_y5_w2_x=5_3 7_2 8_z5_1 7_3$, find $w+x+y+z$.