已知数列\(\{a_{n}\}\)满足\(a_{n+1}+(-1)^{n}a_{n}= \dfrac {n+5}{2}(n∈N^{*})\)，数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)．
\((1)\)求\(a_{1}+a_{3}\)的值；
\((2)\)若\(a_{1}+a_{5}=2a_{3}\)．
\(①\)求证：数列\(\{a_{2n}\}\)为等差数列；
\(②\)求满足\(S_{2p}=4S_{2m}(p,m∈N^{*})\)的所有数对\((p,m)\)．