How to construct the phylogenetic tree of the "High Recombination" genus streptomyces?
You need bootstrap support using a model-based tree building algorhithm, via maximum likelihood (a few people use Bayes). The file format is relaxed phylip format (please submit a separate question if you have difficulties here - its a bit tricky).

I use standard RAxML here, specifically raxmlHPC (easily downloadable and compiles on Linux and OSX). The codes are quite complicated and I've given them below. 

A robust maximum likelihood tree is,

raxmlHPC -m GTRGAMMA -n output.tre -o outgroup-p 10000 -s alignment_file.phy


To make a bootstrap tree,

raxmlHPC -b 459 -m GTRGAMMA -n output.tre -o outgroup -p 10000 -s /path_to_alignment.phy -N 500


This tree will bootstrap for 500 replications, however to start I would use 100 replications.

Make a consensus tree of the bootstraps,

raxmlHPC -f b -m GTRGAMMA -n output.tre -o outgroup -p 10000 -t /path_to_master_tree(best_tree) -z path_to_bootfile


You require bootstrap support >80% and please repeat this with and without 5-2/5-3 (it still looks long)

The cluster you have access to is fine for the calculation, it will take aound 24 hours to complete one bootstrap calculation for one data set and obviously you need to parallelise you calculation across the 22 contigs. 

Viewing the tree, FigTree (for Mac OSX) is easy.

Root

Rooting can be complicated because I don't really know your bacteria.



The recombination issue is more complicated, but I would construct 22 trees from your contigs and assess them for congruence. Panmixia is a concerned, which means too much recombination