Have a check through the forum for problems with the HH5. You might be lucky and have no problems and possibly get a very slight increase in speed but it is by no means certain.
You may be better trying to see if there is a problem with your present set up before deciding to change Homehubs.
Can you run this checker and post back a screen shot of the results
and use this speed tester then carry out the further diagnostics and post back a screen shot of all the results including your IP profile for up and down. This test must be done with a wired connection.
According to the estimator your speeds should be somewhere between the high of Range A which is 30.7Mbps and the low of Range B which is 11.5Mbps.
As you are getting 21Mbps download and 5.8Mbps upload you would appear to be on a Range B line.
There is no point in you being on Infinity 2 because your line can not even attain the maximum for Infinity 1 let alone Infinity 2 speeds. You should consider down grading from Infinity 2 to Infinity 1 if you do decide to recontract.
Because you are within the estimated speeds it is unlikely BT will do anything to help increase the speed you are getting. You are possibly some distance from your cabinet which may account for the relatively poor speeds.