So, the phenomenon you're describing here is called time dilation. Essentially, it says that time passes faster for an object moving very quickly than it does for an object moving slowly or at rest. Additionally, being exposed to a higher level of gravity can slow down the passage of time as well. However, since your question focuses only on speed, we'll ignore gravity for now. The basic formula for time dilation is thus:
\(\displaystyle \displaystyle \Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}\)
This certainly looks intimidating, but I based on the bit of reading I did, I think this problem can actually be boiled down to one of algebra and not require any calculus (unless of course you consider the effects of gravity as well, which DOES appear to need calculus, particularly derivatives). Let's begin by defining the variables and see where that leads us:
\(\displaystyle \Delta t'\) is the time interval passed by the faster moving object
\(\displaystyle \Delta t\) is the time interval passed by the slower [or non-moving] moving object
\(\displaystyle v\) is the velocity of the faster moving object
\(\displaystyle c\) is the speed of light
Now, since the speed of light is defined in meters/second, I feel it would be best to define all the variables in terms of seconds, so make calculations easier. 5 years is 157784760 seconds, 5 minutes is 300 seconds, and the speed of light is 299792458 meters/second. The resulting formula is then:
\(\displaystyle \displaystyle 157784760=\frac{300}{\sqrt{1-\frac{v^2}{\left(299792458 \frac{meters}{second}\right)^2}}}\)
Can you solve the above equation for v? Have a try and see what you get.