50=20/(1+r)+30/(1+r)2+25/(1+r)3+10/(1+r)4+10/(1+r)5,
5=4/(1+r)+6/(1+r)2+5/(1+r)3+2/(1+r)4+2/(1+r)5.
Let y=1/(1+r):
5=4y+6y2+5y3+2y4+2y5,
2y5+2y4+5y3+6y2+4y-5=0.
Let f(y)=2y5+2y4+5y3+6y2+4y-5,
f'(y)=10y4+8y3+15y2+12y+4.
Newton's Method:
yn+1=yn-f(yn)/f'(yn), starting with y0=0:
y1=-f(0)/f'(0)=5/4=1.25, y2=9340/10557=0.8847...
After a few iterations yn becomes the solution for y=0.542420657861.
1+r=1/y, r=1/y-1=0.8435876021821 approx. This is the only real solution for r, but there are 4 complex solutions.