Here's a general answer that will scale up to as many data frames as you have:
library(dplyr)
df_list = list(df5 = df5, df6 = df6)
library(dplyr)
big_df = bind_rows(df_list, .id = "source")
big_df = big_df %>% group_by(Year) %>% summarize_if(is.numeric, mean) %>%
mutate(source = "Mean") %>%
bind_rows(big_df)
ggplot(big_df, aes(x = Year, y = Total, color = source)) +
geom_line()

Naming the list
more appropriately will help with the plot labels. If you do have more data frames, I'd strongly recommend reading my answer at How to make a list of data frames.
Using this data:
df5 = read.table(text = "Year VegC LittC SoilfC SoilsC Total
1 2013 1.820858 1.704079 4.544182 1.964507 10.03363
2 2014 1.813573 1.722106 4.548287 1.964658 10.04863
3 2015 1.776853 1.722110 4.553425 1.964817 10.01722
4 2016 1.794462 1.691728 4.556691 1.964973 10.00785
5 2017 1.808207 1.708956 4.557116 1.965063 10.03936
6 2018 1.831758 1.728973 4.559844 1.965192 10.08578",
header = T)
df6 = read.table(text =
" Year VegC LittC SoilfC SoilsC Total
1 2013 1.832084 1.736137 4.542052 1.964454 10.07474
2 2014 1.806351 1.741353 4.548349 1.964633 10.06069
3 2015 1.825316 1.729084 4.552433 1.964792 10.07164
4 2016 1.845673 1.735861 4.553766 1.964900 10.10020
5 2017 1.810343 1.754477 4.556542 1.965033 10.08640
6 2018 1.814503 1.728337 4.561960 1.965191 10.07001",
header = T)