This works using if statements and adding the strings together.
Just copy and paste it into your sheet.

=IF(R1<1,"NEW","")&IF(AND(R1>0,R1<4),"1-3","")&IF(AND(R1>3,R1<6),"4-5","")&IF(AND(R1>5,R1<11),"6-10","")&IF(AND(R1>10,R1<16),"11-15","")&IF(AND(R1>15,R1<21),"16-20","")&IF(R1>20,">20","")