First, please consider to read How to make a great R reproducible example? and add sample data using dput next time.
df <- data.frame(t = c(1,3,5,2,1,3,4,6,7,2,1))
library(zoo)
library(dplyr)
df$V2 <- rollsum(lead(df$t), 5, align = "left", fill = NA)
df
t V2
1 1 14
2 3 15
3 5 16
4 2 21
5 1 22
6 3 20
7 4 NA
8 6 NA
9 7 NA
10 2 NA
11 1 NA