Mate your current filter is handling all your bioload. When you add a new filter, what happens is that bacteria start to colonise it. At the same time as this happens, there is a precisely equal die off of bacteria in your old filter. At every stage, and no matter how much bacteria is in either filter, the one thing that you know for sure is that the total amount of filtration will always match exactly the needs of the tank.
Therefore, it doesn't matter how ready your new filter is, provided you move both filters (i.e. follow the most important rule- keep the filtration and the fish together).
Longer term the idea behind upgrading filters is that eventually there will be equilibrium between the filters. I submit that this takes about 3 weeks, but you can speed it up (by putting media from the old filter into the new one). At this point, your new filter nay only be supporting 2/3 of the tank's bioload- but the important thing is that there is enough of a colony that when you switch off the old filter it can multiply quickly enough to take up the increase in bioload.
What I recommended (and what I would do) is that you keep both filters running. The advantage of this (aside from the fact you have more filtration), is that if/when you either get new fish, or a fish falls ill/gets injured, all you need to do is get the old tank out of the shed, fill it with water/heat it (have you got a spare heater? Buy one if not), and move the little filter over with the new/ill fish. The big filter will be more than capable of taking the bioload of the main tank, and your quarantine/hospital tank will have a working cycled filter in it from the word go. (Nb: If you do move the little filter over to treat an ill fish, do not then put the filter back on the main tank without either changing media, or boiling the media you have. You don't want to introduce infection to the main tank that way)!
For the record, I never used to bother with quarantine. Then I read a thread on here about some poor girl who wiped out her entire tank with a new fish that was carrying something. I then started being more vigilant about quarantining new fish as a result. Now I don't know what fish you have, but in a 5 footer I guess it's going to be a decent stock list. Consider the hassle and the financial impact of total tank meltdown. You have been presented here with both the opportunity (i.e suddenly having a spare tank and two filters), and the technical/procedural advice (in this post) to introduce proper quarantining measures, if you do not already have them in place.
Hope that doesn't sound too preachy mate, I would just hate to see someone else go through what that poor person in that thread I saw go through!