I assumed you didn't already have an anniversary date field. Then I would approach it by using a formula something like this:
if {?Qtr} = "1" then
(if datediff("q",{empl.hiredate},Date({?Year},01,01)) = 4 then "Qtr1 - OneYear" else
if datediff("q",{empl.hiredate},Date({?Year},01,01)) = 12 then "Qtr1 - ThreeYear" else
if datediff("q",{empl.hiredate},Date({?Year},01,01)) = 20 then "Qtr1 - FiveYear"

else
if {?Qtr} = "2" then
(if datediff("q",{empl.hiredate},Date({?Year},04,01)) = 4 then "Qtr2 - OneYear" else
if datediff("q",{empl.hiredate},Date({?Year},04,01)) = 12 then "Qtr2 - ThreeYear" else
if datediff("q",{empl.hiredate},Date({?Year},04,01)) = 20 then "Qtr2 - FiveYear"

else
if {?Qtr} = "3" then
(if datediff("q",{empl.hiredate},Date({?Year},07,01)) = 4 then "Qtr3 - OneYear" else
if datediff("q",{empl.hiredate},Date({?Year},07,01)) = 12 then "Qtr3 - ThreeYear" else
if datediff("q",{empl.hiredate},Date({?Year},07,01)) = 20 then "Qtr3 - FiveYear"

else
if {?Qtr} = "4" then
(if datediff("q",{empl.hiredate},Date({?Year},10,01)) = 4 then "Qtr4 - OneYear" else
if datediff("q",{empl.hiredate},Date({?Year},10,01)) = 12 then "Qtr4 - ThreeYear" else
if datediff("q",{empl.hiredate},Date({?Year},10,01)) = 20 then "Qtr4 - FiveYear"

else ""
-LB