It's interesting to see how new infrastructure creates It's own demand. M1, M25, Elizabeth Line etc.
Indeed it does. It's why new roads rarely result in much reduction in traffic congestion for very long (or of it does, only locally, with congestion then becoming an issue at the next pinch point).
It's also why cutting rail services is never going to reduce the amount it costs to run the railways. The best thing is to try and run as many services as possible over existing track as possible. As the track is the expensive bit, with the cost difference of a line having 1tpd or 8tph being fairly small. However the income from the latter had the potential to be much higher.
The best way of spending the £5bn would be too enable new city pairings (or to create a metro route), most likely several small schemes.
For example I've previously on other threads suggested a new grade separated junction at Frimley Green to allow a new Basingstoke/Ascot service to run. Add in some extra stations as well and there's likely capacity for the new service to run 2tph (you'd probably consider reducing to 1tph on the Ascot/Aldershot route so as to not have the Camberley level crossing closed too much) serving the circa 250,000 Aldershot Urban Area (Aldershot, Camberley, Farnborough) as a metro for the northern area of that conurbation.
The costly bit would be building the link to allow trains to pass under the main line and loop back up to it to allow trains to avoid crossing on the flat when travelling from Frimley to Farnborough.
You could even extend it so that the service went beyond Basingstoke to increase the frequency of services along the WofE line (probably only as far as Salisbury).
Why? Will the four lines between the junction at Brookwood and just before Basingstoke have spare capacity (typically about 11tph, which in theory should be achievable on just a pair of lines - obviously calling patterns would have an impact on the actual services being run so probably wouldn't work on the existing timetable - but that wouldn't stop new services with limited timetable interfaces from running in the gaps) and so, as long as you can attract enough passengers to more than cover the running costs of the trains you speak the cost of the infrastructure over more services.
If we assume least costs of £220,000 per coach, to run a service with 4 coaches at a frequency of 2tph (in theory it's sub 60 minutes to run between Ascot and Basingstoke, showing for as few extra stops, so it's 4 diagrams being very optimistic) and then assuming that's 1/3 of all costs you're looking at a cost of £11 million a year.
Over 360 days as year, on a 15 hour day with 2tph, and passengers paying an average of £4.50 each way (about the same as half the cost of the anytime return ticket for Basingstoke to Farnborough) then you'd need an average of an extra 110 people using the railways using each of these services.
In perspective that's effectively a doubling of passengers which use Farnborough Main, which could be possible, especially given that there's a few new stations which could generate reasonable passenger numbers on their own right.
See below which demonstrates the possible service timings (I'm not sure if it would fit in the actual network, but by starting at 12:00 it shows more easily the time it would take from end to end):
1200 Ascot
1209 Bagshot
1215 Camberley
1217 Watchmoor Park*
1220 Frimley
1222 Frimley Green*
1225 Farnborough Main
1228 Southwood*
1231 Fleet
1235 Fleet West*
1239 Winchfield
1244 Hook
1252 Basingstoke
1257 Basingstoke Leisure Park*
* Indicates a new station.
Watchmoor Park has a large business park, with limited public transport options, it also had a large Sainsbury's, which whilst you may not get many shoppers using the railways to get there you could have staff use it.
Frimley Green is mostly residential, however not very far away is Frimley Lodge Park which is a fairly popular leisure space. Whilst they won't attract people from out of area, it does make it possible to get to from Frimley and Camberley without using a car.
Southwood is a mixed development (a lot of houses but also quite a bit of business space, for example BMW have a major UK office there - not that a lot of them would use the train). Whilst there would be a lot of passengers, probably a fair number would be changing to London bound services rather than their current drive to Farnborough Main.
Fleet West would serve two new(ish) large developments to the west of Fleet, it would also give easier access to Fleet leisure centre (something which is difficult by public transport without a long walk, from other places within the district of Hart).
Basingstoke leisure park would serve the area around the Milestones museum, it's likely this could be a platform on a siding to allow the services to be turned around away from the main Basingstoke station. Again there wouldn't be a large flow from further afield, but access to the ice rink and cinema by rail could generate reasonable passenger numbers.
Do I know that it could generate the numbers required, no, but given the existing user of railways in the local area and that (whilst in some areas I've probably been fairly optimistic this is somewhere I haven't) it could make rail travel beyond the local area (such at to London) easier. For example, based on off peak ticket prices from Farnborough Main, it would be possible that an extra 35 people (each service) traveling between the service and London would mean no other tickets would be needed to be sold to cover the costs (whilst that's an unlikely number or highlights that there's the potential for significantly higher than £4.50 per passenger of ticket income).
It would mean that between Farnborough and Basingstoke there was 6tph, Farnborough and the existing local stations on the main line would be 4tph and between Farnborough and the Ascot line or the new stations on the main line 2tph (depending on demand your could switch Winchfield with one of the new stations so each had a direct service once per hour to/from London).