This is exponential growth of the form:
f=ir^t, f=final value, i=initial value, r=common ratio, t=time, in this case:
f=5000((100+10)/100)^t
f=5000(1.1)^t
And we wish to know when f=20,886.24 so
20886.24=5000(1.1)^t divide both sides by 5000
4.177248=1.1^t take the natural log of both sides
t=ln4.177248/ln1.1
t≈14.999999574476086460115187057714
t≈15 years (to nearest year)
