How to input nominal values into one column based on values in another column through If_else statements

I am trying to input nominal variables based on a column dedicated to age. Basically, if someone is between the ages of 1 to 5, indicated in the age column, then I want the age group column to have the value of 1, since they are in age group 1. I'm trying to do this in multiple columns since ages increase by one each year. I've tried doing this through a for loop that uses an if else function, but it does not work.

`my_vector_1<-c(1,3,5,7,9,11,2,4,6,8,10,12,3,5,7,9,11,13)

my_matrix_1<-matrix(data=my_vector_1, nrow=6, ncol=3)

colnames(my_matrix_1)<-c(paste0("Age", 2000:2002))

rownames(my_matrix_1)<-c(paste0("Participant", 1:6))

my_data_1<-data.frame(my_matrix_1)

my_data_1<-cbind("AgeGroup2000"=NA, "AgeGroup2001"=NA, "AgeGroup2002"=NA, my_data_1)

my_data_1

#I'm basically trying to make the below code into a for loop

my_data_1$AgeGroup2000[my_data_1$Age2000 %in% 1:5]<-1
my_data_1$AgeGroup2000[my_data_1$Age2000 %in% 6:10]<-2
my_data_1$AgeGroup2000[my_data_1$Age2000 %in% 11:15]<-3

my_data_1$AgeGroup2001[my_data_1$Age2001 %in% 1:5]<-1
my_data_1$AgeGroup2001[my_data_1$Age2001 %in% 6:10]<-2
my_data_1$AgeGroup2001[my_data_1$Age2001 %in% 11:15]<-3

my_data_1$AgeGroup2002[my_data_1$Age2002 %in% 1:5]<-1
my_data_1$AgeGroup2002[my_data_1$Age2002 %in% 6:10]<-2
my_data_1$AgeGroup2002[my_data_1$Age2002 %in% 11:15]<-3`