They may potentially raise an eyebrow at the mised payment but if it shows a good clean record going back and then one blip they will likely put it down to outside factors such as a bereavement or temporary blip. I doubt it will affect you although they may ask about it. This will be helped by the fact that you are putting down a 15% deposit (potentially 10%). Affordability is good and probably would still have been good even with the £5K loan in place.
Potentially if your partner has not held any credit in the last few years then this may cause a problem if they do not have a high enough score to pass the lenders minimum but you possibly won't know this till you apply.
Assuming your partner has held credit of some kind, is on the electoral roll, has held a bank account in the same bank for more than 2 years and all the other little factors that build a score then I cannot see any immediate problem with you getting an accept for what you are looking for.
Be ready to product a form of identity (passport, drivers license) a form of residence (bank statements, utility bill (dated in last 3 months)) and proofs of youer income including payslips for 3 months, P60 for last years (or this years if you have it yet) or SA302's for last 2/3 years if self emploted and 3 months bank statements.
As long as you can verifiy all your info then you should be fine.