What is the sum of the first five terms of the geometric sequence in which a1=5 and r=1/5?

Sum of series of G.P. = Sn = a(1-rⁿ) / 1-r
Here, a = 5
r = 1/5

Substitute their values into the expression:
Sn = 5(1-1/5⁵) / 1 - 1/5
Sn = 5*5/4 [1-1/3125]
Sn = 25/4 [ 3124/3125]
Sn = 781 / 125

In short, Your Answer would be 781/125 in fraction form 
or 6.248 in decimal form

Hope this helps!