Hi L,
Does your current line manager know you are completing L5 and are they aware of your ambitions to progress ? If not, i would try to have this discussion and make it clear you are very keen to take on extra tasks outside of your role which will help with your development. You need to try and gain as much experience as you can where you are. If your company/line manager are not prepared to offer you the chance to gain new skills and develop yourself further, i would potentially be looking for another role at your current level, that has a pathway for career development.

I know it may seem strange to look for another role at your current level, however, experience is the gateway to your progression and you need to find the right employer/role which will help you get there.

I started as general admin, i made my ambitions known, took on lots of extra work and i now work as a HR Manager. Truly, i couldn't have achieved this without a Line Manager who saw my potential and a CEO who provided me with opportunity for growth.

In reply to Hannah:

Hannah's advice is good. if you can agree some development opportunities at your place if work that is the simplest option. Alternatively, you may be able to gain some experience through volunteering. most medium sized charities have HR functions and I dare say would welcome some help! I know we would. however this does have time implications so may not be a viable option for everyone. good luck!

This was myself just over a year ago. I elbowed my way in. Made sure that I discussed my career aspirations with my then line manager, who was fully supportive and allowed me to work closer with the HR Advisors, gaining as much exposure as I could with ER space. Completed my Level 5 last Aug and I am now almost 4 months in an HR Advisor role with a new Company.
You need to be able to demonstrate experience and the only way you will gain that is to get involved in as much as you can and tap into everyone else's experience. Good luck!