Can I Close a 5mm Gap Between my Front Teeth? In How Much Time? (photo)

Your only real option here is to go through braces.   Anything else would be a major aesthetic compromise. Best of luck. 

You can close the gap and correct the over jet with Invisalign or veneers.  The removal of the frenum is very easy and heals quickly with a laser.

Hello, so looking at your pictures.  The muscle attachment is strong and low (called frenum).   The frenectomy was probably recommended because this constant pulling / contracting on the muscle caused diastema (space between teeth).   You can overcome these forces and close the space using Invisalign but you're going to have to wear a retainer- every night, in perpetuity.   Also, all throughout the day, your gap is going to want to open up (the forces are that strong), then all night the retainer will push it back.  This constant movement is not good long term IMO.  I would reconsider the frenectomy.  Second I would investigate if you're a candidate for a lingual bonded retainer on front two teeth.  Hope this helps!