Jackie:
Welcome to Ireland Reaching Out!
I searched the subscription site FindMyPast.ie and found the baptismal records for the five children you listed in the Ballingarry RC parish records. FYI the record for Catherine shows her father was James but when I looked at the register, it appears to be Thomas.
The Ballingarry RC records start in June 1814 so it is possible there were children before Laurence https://registers.nli.ie/parishes/0241 Also, there may have been other children baptized in Ballingarry after 1814 but there were too many Power baptismal records to review. Also did not locate a marriage record and if they were married in Ballingarry a record likely does not exist since the marriage would have been before June 1814.
I did look at the 1850 Griffiths Valuation head of household listing for Ballingarry civil parish and there was no Thomas Power. I did see two Laurence Power record and if Thomas had died, the oldest son would have taken over the lease. http://www.failteromhat.com/griffiths/tipperary/ballingarry.htm
Let me know if you have any questions.
Roger McDonnell
First name(s)LaurenceLast namePowerBirth year-Baptism year1814Baptism date07 Dec 1814ResidenceBallingaryParishBallingarryDioceseCashel and EmlyCountyTipperaryCountryIrelandFather's first name(s)ThomasFather's last namePowerMother's first name(s)AnastaMother's last nameHennesyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000632641#page/1/mode/1upRegisterBaptismRecord setIreland Roman Catholic Parish Baptisms
First name(s)CathLast namePowerBirth year-Baptism year1826Baptism date16 Jan 1826ParishBallingarryDioceseCashel and EmlyCountyTipperaryCountryIrelandFather's first name(s)JasFather's last namePowerMother's first name(s)AntyMother's last nameHenesyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000632641#page/1/mode/1upRegisterBaptism
First name(s)JamesLast namePowerBirth year-Baptism year1823Baptism date08 Jun 1823ResidenceFarnroryParishBallingarryDioceseCashel and EmlyCountyTipperaryCountryIrelandFather's first name(s)ThosFather's last namePowerMother's first name(s)AntyMother's last nameHenesyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//regi
First name(s)MaryLast namePowerBirth year-Baptism year1820Baptism date22 Jul 1820ResidenceBallingarryParishBallingarryDioceseCashel and EmlyCountyTipperaryCountryIrelandFather's first name(s)ThomasFather's last namePowerMother's first name(s)AnastinMother's last nameHennessyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000632641#page/1/mode/1upRegisterBaptism
First name(s)ThomasLast namePowerBirth year-Baptism year1817Baptism date01 Jun 1817ResidenceVillageParishBallingarryDioceseCashel and EmlyCountyTipperaryCountryIrelandFather's first name(s)ThomasFather's last namePowerMother's first name(s)AnastasiaMother's last nameHennesyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000632641#page/1/mode/1upRegisterBaptismRecord setIreland Roman Catholic Parish Baptisms