In[1]:= f[{a_, p_, r_, d_, b_}] := {a+1, b, p^2*(p^2*(231*p^2-315)+105)-5, p*(p^2*(1386*p^2-1260)+210), (d*p-r)/d};

NestList[f, {0., 1., 2., 3., 1.(*<--Need correct initial values for r,d and b *)}, 10]

Out[2]={{0., 1., 2., 3., 1.},

{1., 1., 16., 336., 0.33333},

{2., 0.33333, 16., 336., 0.95238},

{3., 0.95238, 3.09465, 29.0370, 0.28571},

{4., 0.28571, 3.46257, 197.531, 0.84580},

{5., 0.84580, 1.59796, 33.2511, 0.26818},

{6., 0.26818, -6.52096, 15.1710, 0.79774},

{7., 0.79774, 1.00840, 33.9378, 0.69801},

{8., 0.69801, -6.21544, -24.3524, 0.76803},

{9., 0.76803, -1.90085, -52.2697, 0.44278},

{10., 0.44278, -5.25580, -39.1541, 0.73166}}

I am concerned about your not including \[n\] after all your variables in your example code.

I attempted to define a function f that does what I think your RecurrenceTable was doing.

I was not able to convince myself I knew what the initial values for r, d and b should be.

But I was able to use decimal points and carry out the iterations using NestList.

Will this do what you need, after you correct any of my errors or misunderstandings?

This can rapidly do as many iterations as you like, just as long as your initial values all have decimal points.