How many years ago was $5000 invested in an account paying 8% annual interest compounded quarterly, if the amount presently in the account is $11 500

You need a compound interest formula solved for time.
Years = log(total / principal) / n * log (1 + rate/n) where n = 4 for quarterly
Years = log(11,500 / 5,000) / 4 * log (1.02)
Years = log(2.3) / 4* 0.0086001717619
Years = 0.36172783602 / 0.034400687
Years = 10.5151340733 years
Source:
Compound Interest Formulas
http://www.1728.org/compint3.htm