A PIN diode is not a good substitute for a step recovery diode. If you want to bodge (use something cheaper) and I have, then a switching diode like the BA682 (smd) or BA482 (leaded) works much better. This has worked well at 130MHz input to 1500MHz output, but misbehaved at 500MHz in to 3GHz out.
In outline, you need to engineer a low pass filter to the drive side, and a high pass filter to the output side. The first element of the output HPF should be an inductor to ground. It is the current flowing through this inductor that gets interrupted when the SRD 'snaps off' that generates the output voltage. The drive LPF components and the output inductor need to be matched to your input drive voltage and frequency for best efficiency. This part is amenable to straightforward modelling, have a play with SPICE. Note that the diode will draw a unidirectional current, so you need to provide a DC bias path.
It's very easy to accidentally get parametric division of the input signal, unless you can make its environment look lossy at those low frequencies. Unfortunately, parametric misbehaviour is very difficult to model well, especially in the very non-linear environment, and this is where the design can degenerate into black art.
At 5MHz input, you could well expect good behaviour, and good prediction from your simulator.
Unfortunately, if you don't want to afford the 10s or 100s of $ for a specified Step Recovery Diode, other diodes types are not going to spell out in their data sheets whether they are any good or not. It is up to you to do the experiments, and the research.
You have started well, by exposing your assumptions to the views of experts, who have told you that this specific part number of band switching diode works better as a SRD than other types of diode, and especially better than PIN diodes.
Of course if you do not like this advice, there is absolutely no need to take it. What you do need to do is build a model, either SPICE, real hardware, or preperably both, and test some diodes in there.
I draw your attention to the fact that 1N400x and 1N540x diodes are quite snappy, which is why they are often shunted with capacitors in high quality audio amplifier power supplies. Without the capacitor (which slows the rate of change of capacitance versus voltage at end of conduction, the type of behaviour a high doping density will get you in a good rectifier, band switch or step diode, but not in PINs), they often generate a slew of high harmonics of mains which is difficult to eliminate from the audio circuits.