(m^2-5m:m+2)/(m^2-25:m^2-4)=

(m^2-5m÷m+2)÷(m^2-25m÷m^2-4)==m^2-5m÷m+2 × m^2-4÷m^2-25m==m(m-5)÷m+2 × (m-2)(m+2)÷(m-5)(m+5)=m(m-2)÷m+5=m^2-2÷m+5.