The answer would depend on how far the chipmunk is from the fox and its burrow.
Let's say the chipmunk is 20m away from the burrow and the fox is 30m away from the burrow. You can figure this out by computing the time it would take for each animal to reach the burrow.
The formula for speed is:

You can derive the formula for time by exchanging the position of speed (v) with time (t). You new formula would look like this:

Now let's get the chipmunk time first:
Chipmunk given:
v= 5m/s
d= 20m



Now let's get the time of the fox.
Fox given:
v= 8m/s
d = 30m


Since it would take the fox a shorter time to cross that distance then the answer would be:
No, the chipmunk will not make it to the burrow in time.